고등RPM확통해(001~045)

Transcription

1 고등RPM확통해(00~0) 0.. 0: PM 페이지 다민 0DPI 7LPI 하나를 알면 0개, 0개를 풀 수 있는 개념원리수학 RPM 개념원리수학 익힘책 [알피엠] 확률과 통계 정답과 풀이

2 RPM a, b a+b=7, (a, b) (, ), (, ), (, ), (, ), (, ), (, ) a+b=0, (a, b) (, ), (, ), (, ) a+b=, (a, b) (, ), (, ) a+b=, (a, b) (, ),, ++= A, 9 B A;B n(a)=7, n(b)=, n(a;b)=0 n(a'b)=n(a)+n(b)= A, BA;B n(a)=, n(b)=, n(a;b)=8 n(a'b)=n(a)+n(b)-n(a;b) =+-8= 000 A B, B C _= 000 (a+b)(x+y+z+w) a, b x, y, z, w _=8 (a+b+c)(p+q)(x+y) a, b, c p, q, x, y = P = =0 P = = Pº= «P =n(n-)(n-) n(n-)(n-)=0= n= P =0=7 r= «P«=n! 0= n!= n= 0007 P = = != = 0009 P = = ºP =0 9 8= (-)!=!=0 00 (-)!=!= 0 00 A C (-)!=!= A C!!= 00 P = = Pº= = 00 «P =n n == n= 007 P = ==fl r= 008! = =0 0!! 009! = =! 000 (, ), (, ), (, ) 8 (, ), (, ), (, ), (, ), (, ) (, ),, ++=9 00

3 009 ~ 0 00, a, b a-b =0, (a, b) (, ), (, ), (, ), (, ), (, ), (, ), (7, 7), (8, 8) 8 a-b =, (a, b) (, ), (, ), (, ), (, ), (, ), (, 7), (7, 8), (, ), (, ), (, ), (, ), (, ), (7, ), (8, 7) a-b =, (a, b) (, ), (, ), (, ), (, ), (, 7), (, 8), (, ), (, ), (, ), (, ), (7, ), (8, ),, 8++= 00 `a=,b 9 b=,,,,, `a=,b ;(; b=,,, `a=,b b=,,,`,` (a, b) ++= 00, A, B n(a)=, n(b)=0 A;B n(a;b)= n(a'b)=n(a)+n(b)-n(a;b) =+0-=7 00-7= 0=_ 0 0, 0,, (0+0-0)= A B _= A, B _=0, +0= 00,, = 00 = (x+y+z)(p+q+r) _=9 (x+y)(a+b) _= (x+y+z)(p+q+r) (x+y)(a+b) 9+= (x+y+z) (a+b) =(x +y +z +xy+yz+zx)(a+b) _= 007 A, B, C, = =7-7= A B C D = A C B D =, += 009 = = 00

4 RPM, +=8 000 A C B C A = A C B D A = A D B C A = A D B D A 8 0% 0% 0% =,,, +++= 00 B C x A B D_= A C D_=9 A B C D_x_=x A C B D_x_=x ~ A D +9+x+x=+x A D 00 +xæ00 xæ7 B C = _ _ 8 8= _ _ 0 8 _ (+)(+)= 00 00= 00 (+)(+)(+)= _ (+)(+)= -= 0=_ 0«=««(n) 0«(n+)(n+)=(n+) 00 (n+) =00=0, n+=0 n= ,, 0 0,,, 0 0,,,, 0 -= ,,, 000 0,, 000 0,,,,,, 7 0 a= 7-= , 0000, 0000, , 000, , 000, 000, 000, 000, 000, , ,,,, y,, 7 0 b=7-=, a-b=8-=7 7 00

5 0 ~ , 000, 000 x, y, z 00x+000y+000z=7000 x+y+z= yy xæ, yæ, zæ z=, x+y=0 (x, y) (8, ), (, ), (, ), (, ) z=, x+y= (x, y) (, ), (, ), += 007 x, y x+y 8 x+y=, x+y=, x+y=, x+y=7, x+y=8 x+y=, (x, y) (, ) x+y=, (x, y) (, ) x+y=, (x, y) (, ) x+y=7, (x, y) (, ), (, ) fi x+y=8, (x, y) (, ), (, ) fi (x, y) ++++=7 008 x+y+z=yy x, y, z z x, y z x, y z, z z=,,, z=, x+y= (x, y) (, ), (, ), (, ) z=, x+y=9 (x, y) (, ), (, ), (, ) z=, x+y= (x, y) (, ), (, ) z=, x+y= (x, y) (, ) (x, y, z) +++=9 9 z 0% 0% (x, y, z) 0% 009 x+y+z= xæ0, yæ0 z, z z=0,,, z=0, x+y= (x, y) (, 0), (0, ), (8, ), (, ), (, ), (, ), (0, ) 7 z=, x+y=8 (x, y) (8, 0), (, ), (, ), (, ), (0, ) z=, x+y= (x, y) (, 0), (, ), (0, ) z=, x+y=0 (x, y) (0, 0) (x, y, z) 7+++= 000 A BA C A B D A C = A C A D A C BC ED = A, C A, C BA, C D A, C = A, C A CA B, D A, C =8, +8=8 8 00

6 RPM A, C 0% A, C 0% 0% 00 B, D B, D AB, D C, E A, B, D =80 B, D B D B AB, D C, E A, B, D =0, 80+0=0 00 P = 0=0 00 «P +«P =8 n(n-)+n=8 n +n-8=0 (n+7)(n-)=0 n=-7 n= n n= 00 «P «P = «P =«P n(n-)(n-)=n(n-) «P næ n(n-) n-= n=7 007 n n!=0=! n= n «P =0 n(n-)=0=_ n= 008 a f!=0 a f!= 0_= !=!_!_!=8 _8= != P =0 _0= a, e, i t, r, n, g, l a, e, i t r n g l!_ P =!_0=00 A B C D AB E F A B!= A B!= C, D P = = 00 00,, a=!=0, P =, 00

7 0 ~ 0!= b=_= a+b=0+= 00 tuesday t, s, d, y u, e, a!=!= _= 00 sr!= s r P =0 s r!= _0_=70 70 sr 0% s r 0% s r 0% 0% 00 picture i, u, e, p, c, t, r picture 7 7!=00 P _!=0 00-0=00 007!=0 a, b, c a, b, c d, e!_!= 0-= mailbox 7 7!=00 a, i, o m, l, b, x!_ P =0 00-0= % 0% 0% 00 korea k, r o, e, a _= _=, +=!= _= !=70 n n «P =n(n-)!= n(n-)_=n(n-), 70-n(n-)= n(n-)=88, n(n-)==_ n= -= 007

8 RPM 000 0,,,, P =0 _0=00 P =, _=, 00-=7 00 P, P _ P =_= 00,,,,,, (,, ), (,, ), (,, ), (,, ), (,, ), (,, ), (,, ), (,, ) 8_ P =8_!=8 00 0, 0, 0 _ P =,,, 0,, 0 =, +=7 7 0, 0, 0 0%,,, 0% 0% 00 0,,,,,,,,,, 0,,,,,,,, _ P =0,, ++0= a, b, c, d!=9 eab, eac!=, 00 eacdb 00 a!= ba, bc, bd!=8 bea, bec!= bedac,, +8++=7() 007!= 0,!=, 0, 0, 0, C D (-)!=!= C D!= _=8 008

9 0 ~ (-)!=!= P = _= 0070 (-)!=!= P =!=0 _0= (-)!=!=!= a=_=8, b=!= a+b=8+= (0-)!=9! 9!_ 007 (-)!=!!_= (7-)!=! 7!_7= (-)!=! _!=;!;_! a=;!; 007!! 7 0% 0% 0% =!= 0077!!= 0078 (-)!=! _!= P =0!= 0_= P = = 008 P =fi = 009

10 RPM 008 P =fi = P =fl = P = =8 P = = P =fi = 8++= 008 P = P = P =,, ++= , 0 P = _=8 000, P = = P = = = X Y Ya, b, c, d, e x= P = =, X Y Ya, b, c, d, e y= P = =0 x+y=+0= Y,,,,,, P = = 0088! =0!! 0! =0!! 0-0=0!!! 0089 =0! 0090 ` =0!! ` =0!!, 0+0= ! =0!! 0 =! 0-=8 ` 0! =0!!! 0 =!! 0-= 00

11 07 ~ 09, 8+=7 7 0% 0% 0% 009 lll c, h, a, e, n, g, e 7! =0! 009 happiness a, i, e A A, h, p, p, n, s, s 7 7! =0!!!= 0_=70 i i n, t, e, r, n, e, t 7! x= =0!!!, ta A, i, n, e, r, n, e 7 7! y= =0!! y 0 = = 70 x a, e a, e A A, A, b, c, d, f, Aa, e! =0 0! 009 t, m t, ma A, A, o, o, r, r, o, w 8 A t, A m 8! =80!!!,,,, A,,,, A, A, A 7 A, A, A 7! =0 80 0!!! 009 A P =0!!! P B =!! 0_= X, Y, Z P X Q _= P Y Q!! _ =!! P Z Q!! { -}_{ -}=!!!!,, ++= 0098 A B A P B! _ =!! A Q B!! _ =!!!! A R B _= ++= 0099 A B A P B _= A Q B!! _ =0!!!! A R B!! _ =!!!! A S B!! _ =0!!!! fi A T B _= A P A P P Q Z Q R S Y R Q X B B T 0

12 RPM ~fi = 000,, (, ), (, ), (, ), (, ) (, ), (, ) (, ) ++=7 00 (x+y+z+w)(p+q) _=8 (a+b)(p+q) _= 8+= 00 P = = 00 A B, B C, C B, B A,,, = A, 7 B A;B 7, 7 A={, 0,, y, 00} n(a)=0 B={7,,, y, 98} n(b)= A;B={, 70} n(a;b)= 7 A'B n(a'b)=n(a)+n(b)-n(a;b) =0+- = 00 i e!=!= _=8 00 wa!= w a P =0 w a!= _0_=70 007,!_!_= = 7 80 (+)(+)(+)= _7 (+)(+)= -= ,,,, y, , 0 9 -= «P =n(n-)(n-)(n-), «P =n(n-) n(n-)(n-)(n-)=n(n-) n(n-) (n-)(n-)= ( næ) n -n=0, n(n-)=0 n= ( næ) P =_=0 0

13 00 ~ 0 0 (-)!=!!!_!_!_!= 0 Y,, P = =8 0,,, (,,, ), (,,, ), (,,, ), (,,, ), (,,, ), (,,, )! (,,, ) =!! (,,, ) =!! (,,, ) =!! (,,, ) =!! (,,, ) =!!! (,,, ) =! +++++=0 0 A 7 8,,!=,,, 7, 8!=0 _0= B,,,,, _=0,,,, 0 _=, 0+= 0!=0 n «P _! 0-«P _!=8 «P _=, «P = n(n-)=_ n= -= 07 i, i, eaa, A, A, p, r, n, c, p, l 9 9! =00!! 08 (-)!=!= _=0 0 09,,,,,,!! _ =!!! ! =0!! b! =0! 0

14 RPM c! =0! 0-0-0=0 0 0 (-)!=!!_ 0 a!= b!= c!= da!= db!= ++++=8 8 dcabe, 8 dcaeb 8 b 0 a, b a b!=0 a b!= 0_=0 b, c 0_=0 a, b b, c a, b, c!= a c!= _=8,, 0+0-8= a, b 0% b, c 0% a, b b, c 0% a, b b, c 0% 0 _ P =0 _ P =80 P = = A B,, 8! =0!!! A CDB! =! 0-= ,,,,,! =0!!,,,,! =0!, 0+0= % 0% % 0

15 0 ~ 0 07 A B 9! =!! A P! =!! P B! =0!! A PB _0=0-0= A B 0% A PB 0% 0% 08,,,,, (,,, ), (,,, ), (,,, ), (,,, ), (,,, ) (,,, ), (,,, )! _ =8! (,,, )! =!! (,,, ), (,,, )! _ =! 8++=8, (,,, ), (,,, ) (,,, )! =! (,,, )!!! =, +=0 09 p= =0 A B, D C, E _=9 _9= B, D _= C, E _= _=8 q=_(+8)=0 p-q =00 00 f()=0f()= P = = f()=f()= P = = f()=f()=0 P = = f 8 0 0% 0% ++=7 0 A P B A P!! _ =8!!! Q A Q B B!! _ =9!! 8+9=7 E B A D C 0

16 RPM 0 08 H = C = =0 0 0 Cº= C = 8 7 = C = 7 = C = C = n(n-) 0 «C =0 =0 n(n-)=0= n= C + C = + =0+0=0 C = =0 r= ºC = ºC r=r+ r ºC = ºC ºC º = ºC 0-r=r+ r=, r= «C =«C««C«=«C n-= n=8 0 C = =00 0 ºC = =0 C = =0 8 0_0= C = 8 7 = 0 H = C = C = 7 07 H = C = C = = S(, ) S(, ) 0 S(, )= C _ C _ C _ =! S(, )= C _ C _ C _ =! 0 0 P(, ) P(0, ) 0 =++ P(, )= =+++ P(, )= 0 (x+y)fi = Cº xfi + C x y+ C x y + C x y + C xy + C yfi (x+y)fi =xfi +x y+0x y +0x y +xy +yfi xfi +x y+0x y +0x y +xy +yfi 0 (a+b) = Cº(a) + C (a) (b) + C (a) (b) + C (a)(b) + C (b) (a+b) =8a +a b+a b +9ab +b 8a +a b+a b +9ab +b 07 (x+y) C x y x y r= x y C = 08 {a- } fl a C afl {- } = C (-) afl a -r=0 r= C (-) =-0-0 0

17 0 ~ 0 09 (x+y) =x +x y+x y +xy +y yy 00 (a-)fi =afi +a (-)+0a (-) +0a (-) +a (-) +(-)fi =afi -a +0a -0a +a- yy C =«C + C «C = C - C = - = n(n-)(n-), = n(n-)(n-)= n= «C +«C =00 (n+)(n+) (n+)(n+) + =00 (n+)(n+) =00 (n+) =00 n+=0 ( n+æ) n=7 7 0 Cº+ C + C = C + C = C C 0 C + C + C + C = C + C + C = C + C = C 0 «P =0 n(n-)(n-)=0 yy «C = n(n-)(n-)(n-) = yy 0(n-)=0 n-= n= «C +«P = C + P «C +«P = + «C +«P =0+0=80 C 0 C = C r-=r- r=- C = C [ ]= C C = C -r=r- r= 0 «P =0k_ «C «P «P =0k_! 0k=!= k= 07 n n «C «C _=0, «C =8 n(n-) =8, n(n-)==8_7 n=8 08 C = = C = _=0 C = C = =0 C = C = =0, 0+0= Cº= C = C = = ++= 07

18 RPM 00 ()+() ()+() ()+() C = =0 ()+() C = =, 0+= B0 n=0+0=0,, l+m-n=+0-0=- - l 0% m 0% n 0% l+m-n 0% 0 8 C = 8 7 = 0 A B, C C = =0 A C = = n(a)= 7 C = 7 = 0 A, BA, B l= C = A, B A, B m= C = =0 A, B AB C = =0 0 C = =,, C = C = -= 0 C = =0 C = = A=0_=0 9 ªC = = C = C = B=-= 9 ªC = = C = C = C = C=-(+)=0,, A<C<B 07 8 C = C = 8 7 = 08

19 0 ~ 08 A, B C = C = -=0 C = = 9 ªC = =8 C = C = =0 -(8+0)= ºC x x C 0 ºC - x C =0 0 9 x(x-) - =0 x(x-) - =0 x(x-)=0=_ x= 0-=() 09 8 C = =,,!_!= _= C = =0 C = C =!=0 0 0=00 07, C = = 07 n (n-) (n-)(n-) «C =,!= 0 (n-)(n-) =0 (n-)(n-)=0= n-= n= x<y f(x)<f(y) f()<f()<f(), Y,,, f(), f(), f() Y C = C = 07 x <x f(x )>f(x ) f(-)>f()>f(), Y f(-), f(), f() C = = f()=f() f()=f()=, f()=f()=, f()=f()=, f()=f()= f()<f() Y f(), f() 09

20 RPM C = =, +=0 07 f()= x <x f(x )<f(x ) Y,,, f(), f() C = =, Y, 7, 8, 9, 0 f(), f() C = =0 _0=0 0 -=9 08 n n(n-) «C = n n, n n(n-) -n= 08 n «C -n «C -n=0 n(n-) n=8 ( n>0) n(n-) -n=0, n -n-0=0, (n-8)(n+)=0 n(n-) 077 C = = ºC = ºC C = 8 7 =8 079 x,y y C _ C = _=0 O x ªC = 9 8 = - C =-8= ªC = = = C = = 087 7, C - C = 7 - C =-= y O x 08 C = = 088 C = 0 =0 00

21 08 ~ 0, 0 _0=0 0-0=0 0 0% 0% 0% 089, C _ C =_0=0 090, C _ C =_=8, 8+=0 09, C _ C =_=,, 9,, 9++= -= 09 n (n-) «C _«C 0 «C _«C =0 n(n-) (n-)(n-) _ =0 n(n-) (n-)=00=_ _ n= 09 0 H º= C º= C = H =ªC =«C n=9 7 H =ªC =ªC = 9 09 a b μ c «(l+m+n=8) a, b, c 8 H = ºC = ºC = 09 f() f() f(), Y,,, 8, 0 f(), f(), f() f H = C = 097 x, y, z 0 a= H º= C º= C =, x, y, z xæ, yæ, zæ X=x-, Y=y-, Z=z- x+y+z=0 (X+)+(Y+)+(Z+)=0 X+Y+Z=7 X+Y+Z=7, X, Y, Z 7 b= H =ªC =ªC = a-b=-=0 098 X=x-, Y=y-, Z=z- x+y+z= (X+)+(Y+)+(Z+)= X+Y+Z=7, X+Y+Z=7 H =ªC =ªC = 0

22 RPM 099 a+b+c+d=0 (a, b, c, d) a-=a, b-=b, c-=c, d-=d a+b+c+d=0 (A+)+(B+)+(C+)+(D+)=0 A+B+C+D=, A+B+C+D= (A, B, C, D) H =ªC =ªC = a=0, b+c+d=9 (b, c, d) Hª= Cª= C = a=, b+c+d=8 (b, c, d) H = ºC = ºC = a=, b+c+d= (b, c, d) H = C = C = a=, b+c+d=0 (b, c, d) Hº= Cº= +++= 00 e A {a, b, c};{c, d}={c}, A A,, 00 S(, ) A={,,, 7} S(, )= S(, ) A={}'{,, 7}={}'{,, 7}={}'{,, 7} ={7}'{,, }={, }'{, 7}={, }'{, 7} ={, 7}'{, } S(, )=7 S(, ) A={}'{}'{, 7}={}'{}'{, 7}={}'{7}'{, } ={}'{}'{, 7}={}'{7}'{, }={}'{7}'{, } S(, )= S(, ) A={}'{}'{}'{7} S(, )= A S(, )+S(, )+S(, )+S(, ) =+7++= 00 8, a= C _ C _ =! 8, b= C _ C = b-a=-= 00 a=ªc _ C _ C =0 b=ªc _ C _ C _! b=78 c=ªc _ C _ C _! b=80 a-b+c= =0 0 a 0% b 0% c 0% a-b+c 0% 00, S(, ),, C _ C _ C _ =0!,, C _ C _ C _ =!, 0+= 0

23 0 ~ 0 00, S(, ),, C _ C _ C _ =!,, C _ C _ C =0,, C _ C _ C _ =!,, +0+= S(, )+S(, ) S(, ),,, C _ C _ C _ C _ =0! S(, ),,,, C _ C _ C _ C _ C _ =!, 0+= 00 (,, ) (,, ) C _ C _ C _ + C _ C _ C _!! =0+=!= _=0 0 0,, C _ C _ C!=90! P = 90_=0 0 0% 0% 0% 008 (,,,, ) C _ C _ C _ C _ C _ =! (,,,,, ) C _ C _ C _ C _ C _ C _ =!, += 009,, C _ C _ C _ =!!= _=90 0 (,, ) (,, ) A, B, C (,, ) { C _ C _ C _ }_!=0! (,, ) { C _ C _ C _ }_!=90!, 0+90= , C _ C =, C _ C _ =!, 0

24 RPM C _ C = = 0, C _ C =, C _ C _ =! _= 0, C _ C _ =0!, C _ C = 0 = P(8, )+P(8, )+P(8, ) 8=8 =7+=+=+=+ =++=++=++ =++=++ P(8, )+P(8, )+P(8, )=++=0 a=0, 8 P(8, ) 8=+++=+++ =+++=+++ =+++ b=p(8, )= ab=0_= =+++++=+++++ =+++++=+++++ =+++++ P(0, )= 0 7 0= = = P(0, 7)= 0 8 0= = P(0, 8)=,, P(0, )+P(0, 7)+P(0, 8)=++= =++=++=++ 7 7=+, += =7++=++ =++=++ =++=++ =++ P(9, )=7 9 9, = =+=+ P(, )=, P(, )= P(, )+P(, )= 7 00 {mx + } fi x C (mx ) { } -r = C m r x r- x r-= r= C m x =0m x 0m =80 m= 0 {ax + } x C (ax ) { } = C a x fi x 0

25 0 ~ 0 x -r= r= x C a = a = a= {ax + } 0% x r 0% a 0% 0 (x-) C x (-) (x+)fi Cπ(x)fi π = Cπ xfi π fi π (x-) (x+)fi C Cπ(-) fi π x π yy x 8-r-p=, r+p= (r, p) (, ), (, ), (, ) x C C (-) + C C (-) + C C (-) =-+0-0 = (x-y)fi C (x) (-y)fi = C (-)fi x yfi x y r= C (-) =80 ('+x)fl C (') -r x -r=0 -r= -r= -r= r= r= r= r=0 C (' ) + C (' ) + C (' ) + Cº(' )fl = = n C r (x ) n-r { } r = n C r r x n-r x n-r=0, n n=r n n=, 0,, y n 0 {x+ } fi, (x +) x C x fi, Cß x ß {x+ } fi (x +) x C Cß x ± ß fiyy x r+s-=, r+s= (r, s) (0, ), (, ), (, ), (, 0) x Cº C + C C + C C + C Cº =++0+0 = 0 (x+a), {x- } x C a x, Cß x ß {- } ß (x+a) {x- } x x C Cß a (-)ß x ß yy r-s+=, r-s=- (r, s) (, ) x C C a (-) =-7, -8a =-7 a = a= ( a>0) 07 {x+ } fl x C xfl { } = C xfl yy x (x +x+){x+ } fl x x, x, x x -r=-, r= x C x = x -r=- x 7 r= r 0 r x -r=0, r= C x =0,, x +0= x 0

26 RPM 08 +x, +x (+x){(+x) -} (+x)- = x x (+x) x (+x) C x x r= x C = x 09 (+x)+(+x) +(+x) +y+(+x) (+x){(+x) -} (+x) -x- = = (+x)- x x (+x) x a = C 00 (+x )+(+x ) +(+x ) +y+(+x )fl (+x ){(+x )fl -} (+x ) --x = = (+x )- x x (+x ) x (+x ) C (x ) = C x r= r= x C 0 x (+x )+x (+x ) +y+x (+x ) x (+x ){(+x ) -} = =(+x ) -(+x ) (+x )- xfl (+x ) xfl (+x ) C (x ) = C x r= r= xfl C (+x) --x x 0 (+x+x )fl!! π xœ (x ) = p!q!r! p!q!r! xœ ± (, p+q+r=, pæ0, qæ0, ræ0) xœ ± =xfl q+r= (p, q, r) (0,, 0), (,, ), (,, ), (, 0, ) xfl!!!! =!!!!!!! 0 (x-y+z)fl!! xπ (-y)œ (z) = p!q!r! p!q!r! (-)œ xπ yœ z (, p+q+r=, pæ0, qæ0, ræ0) x yz p=, q=, r=! (-) =-0!!! 0 (x +ax+)!! (x )π (ax)œ = p!q!r! p!q!r! aœ x π ±œ (, p+q+r=, pæ0, qæ0, ræ0) x π ±œ =x p+q= (p, q, r) (0,, 0), (,, ) x 7!! a + 0!!0!!!! a =7 a +a=7, a +a-7=0, (a-)(a +a+7)=0 a= 0 C 0 = C 0 n- C r- + n- C r = n C r C 0 + C + C + C + C + C =( C 0 + C )+ C + C + C + C =( C + C )+ C + C + C =( C + C )+ C + C =( C + C )+ C = C + C = 7 C = 7 C 0 {x +x- } x 7! (x )π xœ {- p!q!r! } x 7! = p!q!r! (-) x π ±œ (, p+q+r=7, pæ0, qæ0, ræ0) x π ±œ =x p+q-r=0 p=, q=, r= 7! (-) =80!!! 07 «C +«C =«C «C =«C, «C =«C«=«C n-= n= C = C ()= C + C + C + C +y+ 0 C = C + C + C +y+ 0 C = C + C +y+ 0 C = 0 C + 0 C = C 0

27 0 ~ Cº C C + 8 C + 9 C + 0 C + C = 7 C C + 8 C + 9 C + 0 C + C =( 7 C C )+ 8 C + 9 C + 0 C + C =( 8 C + 8 C )+ 9 C + 0 C + C =( 9 C + 9 C )+ 0 C + C =( 0 C + 0 C )+ C = C + C = C C - Cº= C - 09 n nc 0 n C n C y n C n nc 0 + n C + n C +y+ n C n =«n C =0 n=0 0 0 ( -) «= =0 0 n= - 00 «Cº+«C +«C +y+«c«=««c +«C +y+«c«=«- 00<«-<00 fl =, =8, = n=7 0 ªªCº+ªªC +ªªC +y+ªªc ª =ªªCªª+ªªCª +ªªCª +y+ªªc º, ªªCº+ªªC +ªªC +y+ªªcªª= ªªCº+ªªC +ªªC +y+ªªc ª= = log (ªªCº+ªªC +ªªC +y+ªªc ª)=log =98 f(n)= ( C + C + C +y+ C ) C + C +y+ C = n («-) f(n)= = = («-) k= - f()=;@;(fi -)= n k= 0 (ªC ) k=0 =ªCº ªCº+ªC ªC +ªC ªC +y+ªcª ªCª =ªCº ªCª+ªC ªC +ªC ªC +y+ªcª ªCº (+x) (+x), (+x) x Cª n=8, r=9 n+r=7 7 0 (a+b) 0 0 = 0 C k a k b 0-k a= b= k=0 0 0C k { } k { } 0-k ={ + } 0 = 0 = 0 k=0 P= log P=log =0 0 ( ºC ) = ºC ºC º 0 (+x) (+x) =(+x) x ( ºC ) = ºC º 0 x 0 (+x)fi = ºCº+ ºC x+ ºC x +y+ ºC º xfi x=i ºC º (+i)fi = ºCº+ ºC i- ºC -y- ºC º =( ºCº- ºC + ºC -y- ºC º) +( ºC - ºC + ºC -y+ ºC ª)i (+i)fi ={(+i) } fi =(i) fi = fi i ºCº- ºC + ºC -y- ºC º=0 a=0 ºC - ºC + ºC -y+ ºC ª= fi b= fi a+b= fi fi 0 a º (+x) =(+x) (+x) x a º= ºCº ºC º+ ºC ºCª+ ºC ºC +y+ ºC º ºCº «C =«C«a º= ºCº ºCº+ ºC ºC + ºC ºC +y+ ºC º ºC º 0 = ( ºC ) k=0 0 0 k=0 k=0 0 k=0 07 (+i) fl = Cº+ C i+ C i +y+ C i fl = Cº+ C i- C - C i+y+ C =( Cº- C + C -y+ C ) +( C - C + C -y- C )i (+i) fl ={(+i) } =(i) = Cº- C + C - C +y- C + C = (+i) fl 0% 0% 0% 07

28 RPM 08 «C =«C «C«=«C r= n-r= yy ºC = ºC ºC º = ºC 0-r=r- r=7 n= n+r=+7= C = ,, C _ C =0_=0!= P = 0 =0 0, H = C = C =8 0 8 P(8, ) 8 8=+++ =+++ =+++ =+++ =+++ P(8, )= 0 8 (,, ), (,, ) C _ C _ C _ + C _ C _ C _!! =0+80 =90 A, B, C!= 90_=90 0,,, H = C = C =, H = C = C = -=0 0 C 0 + C + C + C + C + 7 C + 8 C + 9 C 7 = 0 C 7 C + C + C + C + 7 C + 8 C + 9 C 7 = 0 C 7 - C 0 = 0 C 7-0 ºC 0-r = ºC 0-r =(+) - ºCº = - 07 C + C + C +y+ ºC =( C + C )+ C +y+ ºC =( C + C )+ C +y+ ºC = C + C + C +y+ ºC =( C + C )+ C +y+ ºC = C + C +y+ ºC = C n=, r= n+r=+= 08 (+x)«= «C x x «C «C = 0 r= n(n-) = n -n-90=0, (n-0)(n+9)=0 n=0 ( n) n r=0 0 r= 0 08

29 08 ~ (x+)fi, (x-) C (x) fi, Cß xß (-) ß (x+)fi (x-) C Cß fi (-) ß x ±ßyy x r+s= (r, s) (0, ), (, ), (, 0) x Cº C fi (-)+ C C (-) + C Cº (-) = (+x)+(+x) +(+x) +y+(+x) (+x){(+x) -} (+x) -x- = = (+x)- x x (+x) x (+x) C (x) = C x r= _ C _ =0 0 {x - } «x «C (x )«{- } =«C (-) x «fi x x «fi =x n-r=0 n-r=0 nr= n= p= C (-) =0 q=0 p+q=+0= 0 0 C C + 0 C +y+ 0 C C 0 = 0C 0 = -= 0 C C + 0 C +y+ 0 C 9 (+x) n = n C 0 + n C x+ n C x +y+ n C n x«x=-, n= C 0 - C + C - C + C =0 (+x) n = n C 0 + n C x+ n C x +y+ n C n x«x=-n=7 7C 0-7 C + 7 C - 7 C + 7 C - 7 C + 7 C - 7 C 7 =0 7 C 0 = 7 C 7 7C + 7 C + 7 C = 7 C + 7 C + 7 C, 0 «Cº+7 «C +7 «C +y+7««c«=(+7)«=8«= «log («Cº+7 «C +7 «C +y+7««c«) =log n =n 0 x+y+z< x, y, z (x, y, z) x+y+z=0 Hº= Cº= x+y+z= H = C = x+y+z= H = C = x+y+z= H = C = C =0 fi x+y+z= H = C = C = fi +++0+= 0 A, B, C!= 9,, ªC _ C _ C _ =80!!= 9 80_=80, _80=k k= =0 =9+=8+=7+=+=+ =8++=7++=++ =++=++=++ =++=++ P(0, )+P(0, )+P(0, )=++8=! 07 (x) {- } (z) =-080!!! y x z y x z -080 y 09

30 RPM 08 (,, ), (,, ), (,, ) (,, ) { C _ C _ C _ }_!=90! (,, ) ( C _ C _ C )_!=0 (,, ) { C _ C _ C _ }_!=90!,, =0 09 f() f() f() f() f Y7 f(), f(), f(), f() f 7 H = ºC =0 070 C =9 C _= 8 C _ C _=9 9 C _8_ªC =7 9-(+9+7)= 07 0 MB CD CD (, ) C _ C _ =! (, ) {0 MB, (00 MB, 00 MB, 00 MB)} =00(MB), {00 MB, (0 MB, 00 MB, 00 MB)} =00(MB) CD0 MB ( C _ C )-= += CD (,, ) C _ C _ C _ =!, += 07 9 ªC =8 C =0 8-0=, C _ C =_=8, C _ C =_= 8+= 07 {x+ } fl x C xfl { x } = C xfi fl 0% 0% -r=0 r= a= C =0, x -r= r= b= C =0 a+b=0+0=0 0 00

31 00 ~ 0 {x+ } fl 0% x a 0% b 0% a+b 0% 07 (+x)«x, x, x «C, «Cª, «C º «C +«C º= «Cª n! n! n! + = 8!(n-8)! 0!(n-0)! 9!(n-9)! 0!(n-8)! n! 0(n-8)=0_9+(n-8)(n-9) n -7n+=0, (n-)(n-)=0 n= n= n+=7 7 «C «Cª«C º 0% 0% n 0% n 0% 07 0=+ 0=++=++=++=++ 0=+++=+++=+++ =+++=+++=+++ = =++++=++++ =++++=++++ =++++= =8 8 0% 0% 0% 0% 0% 07 X Ya, b, c f()=b X,,,, Y a, b, c a, c X,,,, (,, ) (,, ) (,, ) { C _ C _ C _ }_!=0! (,, ) { C _ C _ C _ }_!=90! X,,,, (, ) (, ) (, ) ( C _ C )_!=0 (, ) ( C _ C )_!=0, = ,,, 7, 8 C = 0

32 RPM C =, C _ C _ =! = B B,, C _ C _ C =0 B, C _ C _ =0!, 0+0= ,,, C =,, C _+ C _=8,, C _= C = +8++= 0 080,,,,, {,,,,, } {,, } {,,,,, } {,, } 08 =8 H, T A={THH, HTH, HHT} B={THH, HTH, HHT, TTH, THT, HTT, TTT} A;B={THH, HTH, HHT} BÇ ={HHH} C={HHH} A;C=Δ, B;C=Δ A C, B C 08, 08, = =9 9 = 08 (, ), (, ), (, ) (, ), (, ) (, ) ++= = 08!=0 0

33 0 ~ 0 A!= = 0 08!=0 D, E! D, E! D, E!_!=8 8 = = P(A'B)=P(A)+P(B)-P(A;B) = + -P(A;B) P(A;B)= 090 P(A'B)=P(A)+P(B) 0.7=0.+P(B) P(B)= A, B 0 P(A)=,P(B)=,P(A;B)= P(A'B)=P(A)+P(B)-P(A;B) 0 P(A'B)= P(A'B)= = 0 09 A, B P(A)=,P(B)=,P(A;B)= P(A'B)=P(A)+P(B)-P(A;B) P(A'B)= P(A'B)= = , A AÇÇ P(AÇ )= 8 7 P(A)=-P(AÇ )=- = A AÇ AÇ ={(, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, )} 9 P(AÇ )= = P(A)=-P(AÇ )=- = 09 A AÇ C P(AÇ )= = C 0 9 P(A)=-P(AÇ )=- = A AÇ ={,,,, 7, 8, 0} B BÇ ={,,, 8, 9, 0} A, B C AÇ ;BÇ ={,, 8, 0} C = 097 A={,, }, B={,, }, C={, } A;B=Δ, B;C={}, A;C={} A B 098 A={,, } B;AÇ =B-A={, } A;(B;AÇ )=Δ BÇ ;C=C-B={} A;(BÇ ;C)=Δ B;CÇ =B-C={} A;(B;CÇ )=Δ,, A ,, 0

34 RPM 099 n n n 8 n =8, n = n= (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ), (, ) 7 ;!&; ;!&; 000, _= (, ), (, ), (, ), (, ), (, ), (, ) (, ), (, ), (, ), (, ) (, ), (, ),, ++= = 00 A C A C A B C_=() = + 00 A fl =, fl = = ;!^;=;!; 00, _= x +ax+b=0 D D=a -b<0, b> a (a, b) (, ), (, ), (, ), (, ), (, ), (, ), 00!!_!!_! =! 00! P =! _! =! ! c r!_ P _!!_ P _! = 8! 8 8 8! P _!_! P _!_! = 8! 8 007,,,! 000!!!+!! = (7-)!=! A B (-)!_!=!_ 0

35 0 ~ 08!_! = 8!_ = 9!_ (8-)!=7! (-)!=!!!_!!_! = 7! 00 (-)!=! (-)!=!!!_! P =!!_!+! =! 0% 0% 0% 0% 0 0 (0-)!=9! 9!_,, 8 8!,, 8!_ 0 X Y f P = = x +x f(x )+f(x ), P = = = 0 A, B, C, D P = = P = = 8 0 P = =7 (,, ), (,, ), (,, ) -(_)=8 8 = 7 0,,,, P = = 00,, _ P =_ =7, _ P =_ =0, 7+0= = 0 A B 8! =70!! A C B!! _ =0!!! 0

36 RPM 0 = SCHOOL! =0! O!=0 0 = CECILIA 7! =0!! C, C, L, E, I, I, A (,,,,,, )! =,!! =! _= = 0 09 X X P = = 7! (,,, ) =!! (,,, ) =!! (,,, ) =! ++ =; ; ; ; 00 C =0 B F B, F B C = ; 0;=; 0; 0 C =0 C E C, E C C = ; 0; ; 0; 0 C =0 ()_()_() C = ; 0; 0 0 ºC =, C _ C =_0=0 0 0 = 0 0%, 0% 0% 0 0 ºC C _ C C _ C ºC = 0 ºC, n «C «C =, «C = ºC ºC 9 9 n(n-) = 90, n(n-)=0= 9 n=

37 08 ~ 00 0 C =0 = O C =0 O _= ;!0@;=;#; ;#; 07 x+y+z=0x, y, z 0 H º= C º= C = A=x-, B=y-, C=z- Aæ0, Bæ0, Cæ0 x+y+z=(a+)+(b+)+(c+) =A+B+C+=0 A+B+C=, A+B+C= H = C = C = ;!%;=; ; ; ; 08 n, «C ºC «C n(n-) =, = ºC 90 n(n-)=0= n= 09 0 B 7 7 = =() = 00 () 0 () n n 0.0= 00 n=0.0_00= 0 BC A P D PBC P B C = 0 p =p p+(9-)p=p p = p 8 0 AB _= ax+by= xy S S= = a b ab=8 ab=8 (a, b) (, ), (, ) = 8 0 AB =aac =xad =y 0 x a, 0 y a CD AB A x y a C y b O ax+by= D a 8 B x 07

38 RPM x-y a a -a = a 0 P(A'B)=P(A)+P(B)-P(A;B) P(A'B)= + -P(A;B) P(A'B) + -P(A;B) P(A;B)æ + -= P(A;B) 07 P(A'B)=P(A)+P(B)-P(A;B) P(A'B)= + - P(A'B)= 0 08 A, BA;B, A={,, 9, y, 99} n(a)= B={, 0,, y, 00} n(b)=0, A;B={, 0,, y, 90} n(a;b)= P(A'B)=P(A)+P(B)-P(A;B) 0 7 P(A'B)= + - = An(A) 0% Bn(B) 0% A;B 0% n(a;b) 0% y a a O a a x 09 A B P(A)=0., P(A;B)=0., P(A'B)=0.8 P(A'B)=P(A)+P(B)-P(A;B) 0.8=0.+P(B)-0. P(B)=0. 0 % 0 % 00 0 ºC C AP(A)= ºC C BP(B)= ºC C CP(C)= ºC A, B, C P(A'B'C)=P(A)+P(B)+P(C) C C C P(A'B'C)= + + = ºC ºC ºC 0 S=A'B P(A'B)= P(A'B)=P(A)+P(B) = +P(B) P(B)= 0!=!=!=!=!= +++ = ;!; 0 0 ºC =0 A, B C _ C P(A)= = 0 C P(B)= = 0 A, B P(A)+P(B)=;!;+;!;=;@; A, B, C 08

39 0 ~ 0 C C P(A)= = ªC 8 C C P(B)= = ªC C P(C)= = ªC 8 A, B, C P(A'B'C)=P(A)+P(B)+P(C) P(A'B'C)=;!8%;+; ;+;8 ; P(A'B'C)=;!^; ;@; ;!^; 09 B D TB D TÇ!_! P(TÇ )= =! P(T)=-P(TÇ )=-;@;=;#; ;#; 00 0 ºC (0-n) º «C -;!#;=; ; 0 A AÇ C C P(AÇ )= _ = C C 9 º «C =, º «C = ºC ºC º «C =, (0-n)(9-n)= n -9n+78=0, (n-)(n-)=0 n= ( n 0) P(A)=-P(AÇ )=-;9!;=;9*; 0 A AÇ C P(AÇ )= = ºC 8 P(A)=-P(AÇ )=-;@8!;=;!8&; ;!8&; 0 A AÇ C P(AÇ )= = C 0 P(A)=-P(AÇ )=-; 0;=;!0(; 07 A AÇ C P(AÇ )= = ºC P(A)=-P(AÇ )=-;!;=;@; 08 A AÇ P _! P(AÇ )= =! 0 P(A)=-P(AÇ )=-; 0;=; 0; 0 ;@0(; -;@0(;=; 0; 0 x º x C = ºC 0 ºC 0 º x C = = = 0 0 º x P! = º x P = = = P 0-x= x= 0 -() =-{()+( )} =-{ + } =;!#; ;!#; 0 P(AÇ 'BÇ )=P((A;B)Ç )=;%; P(A;B)=-P((A;B)Ç )=-;%;=;!; P(A'B)=P(A)+P(B)-P(A;B) P(A'B)=;!;+;!;-;!; 09

40 RPM P(A;B) 0% P(A'B) 0% 0 A AÇ P(AÇ )=()+() P(AÇ )=-() A={,, }, B={,, } P(A)=;!;, P(B)=;!; P(A)+P(B)= A;B={, }+Δ A B () 09 (,, ), (,, ), (,, ), (,, ), (,, ), (,, ), (,, ) 7, P(AÇ )=;!0);+; 0;-; 0;=;!0#; ;7!; P(A)=-P(AÇ )=-;!0#;=; 0; 0 A AÇ C P(AÇ )= = ªC 8 P(A)=-P(AÇ )=-;8 ;=;8*#;! A AÇ!_! P(AÇ )= =! P(A)=-P(AÇ )=-;!;=;@; 00 A={(, ), (, ), (, ), (, ), (, ), (, )} B={(, ), (, ), (, )} C={(, ), (, ), (, ), (, )} D={(, ), (, ), (, ), (, ), (, )} A;B=A;D=B;D={(, )} A;C=Δ, B;C=Δ, C;D={(, ), (, )} A C, B C 0 ( ) =-() C =- ºC =-;!;=;%; 0 0 P(A) () 0 P(A), 0 P(B) 0 P(A)+P(B) () P(S)=, P(Δ)=0 -P(S)=P(Δ) (), ;8*#; ;@; 0 0 ºC = A AÇ C =0 P(AÇ )=;!);=;9@; 07 0 P(A) (),,,, 08 () S={a, b, c, d, e, f}, A={a, b, d, f }, B={c, e, f }A'B=S P(A)+P(B)=;$;+;#;=;&;+ () () A, B P(A)=-P(AÇ )=-;9@;=;9&; 0 8 (8-)!=7! ;9&; P =!! 7! =

41 0 ~ 0 C 0 ºC C =- = ºC 0 BANANA! =0!! N! =0! 0 = 0 0 CDCD A, CD B, CD C C C P(A)= =, P(B)= =, ºC 0 ºC 0 C P(C)= = ºC 0 A, B, C P(A'B'C)=P(A)+P(B)+P(C) P(A'B'C)=; 0;+;!0;+;!0; P(A'B'C)=; 0; 07 (+n) ; 0; C 7 =- =, = «C 0 0 (n+)(n+) 0 (n +n+)=0, n +n-=0 (n+7)(n-)=0 n= 08 = P = =0 0 = 9 P(A'B) P(A)+P(B) (, P(A;B)=0 ) () P(A'B) P(A)+P(B)-P(A;B) P(A;B)æP(A)+P(B)- (), 070 x +ax+b=0 D D, =a -bæ0 b a a= b= a= b=,,, aæ b=,,,,, _= = _ 07 b, r, o, a, d, c, a, s, t 9 9!! a, a 8! a, a 8! = 9! 9! -;9@;=;9&; 07 _= ()+() ()+() _+_=8 P(A)=;!*;=;!; _= P(B)=-;@%;=;!!;, A;B={(, ), (, ), (, ), (, ), (, )} P(A;B)=; ; n(a) n(b) 09 P(A)=, P(B)= n(s) n(s) A,B P(A) P(B)() P(A'B)=P(A)+P(B)-P(A;B) P(A'B)=P(A)+P(B)-P(A;B) =;!;+;!!;-; ; =;@$;=;@; ;@; 0

42 RPM ! =0!!,,,,, (,,,,,, ),!! _ =!! = 0 07 P A AÇ P(AÇ )= P(AÇ )=;8 0; P(A)=-P(AÇ )=-;8 0;=;8&0#; 07 A, B P(A;B)=0, A'B=S P(A'B)=P(S)= P(A'B)=P(A)+P(B)-P(A;B) P(A'B)=P(A)+ P(A)-0( P(A)=P(B)) P(A'B)= P(A)= P(A)= P + P + P P ;8&0#; 07 A B 7 P(A)=, P(B)=, P((A'B)Ç )= P(A'B)=-P((A'B)Ç ) P(A'B)=- = P(A;B)=P(A)+P(B)-P(A'B) 7 8 P(A;B)= + - = 077 _ P =00 0 0,, A, B, C P P(A)= = 00 _ P(B)= = 00 _ P(C)= = 00 A, B, C P(A'B'C)=P(A)+P(B)+P(C) P(A'B'C)= + + P(A'B'C)= 078 A B 0!!! A P B!!!!!!!! 0!!!!! = ºC =0 C =0 0-0=0 ;!!0);=;!!; 080 a, b, c, d,!= 0

43 0 ~ 07 c d, a, c, b d, b, c, a d!= + = 08 0,,,, P =9, 00, 0,, P = 0,, P =8, 00 +8= ;9$@;=; ; ; ; P(A'B) 0% P(AÇ ;BÇ ) 0% 08 9, A AÇ C C C P(AÇ )= + ªC ªC P(AÇ )=;@);+;%; P(AÇ )=; ; P(A)=-P(AÇ ) P(A)=-; ; P(A)=;ª; ;ª; 08 (a-b)(b-c)(c-a)=0 X (a-b)(b-c)(c-a)+0 XÇ (a-b)(b-c)(c-a)+0 a, b, c P P(XÇ )= = 9 P(X)=-P(XÇ )=-;9%;=;9$; ;9$; 08 P(A'B)=P(A)+P(B)-P(A;B) P(A'B)= P(A'B)= 8 P(AÇ ;BÇ )=P((A'B)Ç ) P(AÇ ;BÇ )=-P(A'B) P(AÇ ;BÇ )=- 8 P(AÇ ;BÇ )= 8 8 0% 0% 08, =,,, y,,, 7, (, ), (, ), (, ), (, ) 7 (, ), (, ), (, ), (, ), (, ), (, ) (, ), (, ),,, 7, ++= = 0

44 RPM, 0% 80% 0% μ «=, μ «= m+n=9 m, n m, n (m, n) (, 7), (, ), (, ), (, ) m=, n=, mn n C 8 «C = C 8 «C = C 8 n(n-) = 8 n -n-0=0, (n-)(n+)=0 n= ( n>0) 0% 0% 70% 089 f:a B f()<f()<f()=f() fb={,, 7, 8, 9, 0} C C = 090 P AB PAB PPAB -;!; p = ABCD 8-p = 8-p 8 8 D A P P C B 087 X Y f P = =8 k=0 f(k)=f(0)+f()+f()+f()= Y={0,, } f {0,,, } {0, 0,, } X={0,,, }!! =, =!! f += m μ, n «0

45 0 07 ~ P(A'B)=P(A)+P(B)-P(A;B) P(A'B)= + - = 09 A={,, } P(A)= = 09 A={,, }, B={,, } A;B={} P(A;B)= P(A;B) P(A) 09 P(B A)= = = 09 A, 0 B P(A)=,P(A;B)= 8 8 P(A;B) 8 P(B A)= = = P(A) 8 09 P(A;B)=P(A)P(B A)= = 09 P(A;B)=P(B)P(A B)=0._0.=0. 0. P(A;B) P(A) P(B A)= = = 098 P(A'B)=P(A)+P(B)-P(A;B) P(A'B)= =0. P(AÇ ;BÇ )=-P(A'B)=-0.=0. 0. P(AÇ ;BÇ ) P(AÇ BÇ )= = =0.7 P(BÇ ) P(A)=,P(B)=,P(A;B)= 0.7 P(A;B)=P(A)P(B)= = A, B 00 P(A;B)=P(A)P(B) P(A;B)= = 00 P(AÇ ;B)=P(AÇ )P(B)={-;!;} ;!;=;!; 00 A, B ;!; P(A BÇ )=P(A)=;!; ;!; 00 A A, B BA, B P(A;B)=P(A)P(B)=0._0.7= A, BA, B P(A;B)=P(A)P(B)= = 007 P(A)= = 008 P(A)=,P(AÇ )= ºC { } fl { } 0 0 = 009 A P(A)=;!; C { } = 00 A P(A)=, C { } = 0 A P(A)=0.8 C (0.8) _0.=

46 RPM 0 P(A'B)=-P((A'B)Ç ) P(A'B)=-P(AÇ ;BÇ ) P(A'B)=-0.=0. P(A;B)=P(A)+P(B)-P(A'B) P(A;B)= =0. P(A;B) 0. P(A B)= = = P(B) 0. P(AÇ Ç ;BÇ )=P((A'B)Ç )=-P(A'B) P(AÇ Ç ;BÇ )=-;@;=;#; P(AÇ Ç ;BÇ ) P(AÇ BÇ )= = P(BÇ ) P(AÇ BÇ )=;#; ;!; ;#; 0 P(A)P(B A)=P(B)P(A B) P(B A)= P(B A)= 0 A, B A;B=Δ B,AÇ B;AÇ =B P(B;AÇ ) P(B) P(B AÇ )= = P(AÇ ) -P(A) P(B AÇ )= = = - P(A;B) 0 P(B A)= P(A) P(A;B)=P(A)P(B A)= = P(A;B) P(A B)= P(B) P(A;B) P(B)= = = P(A B) P((A-B)'(B-A)) =P(A-B)+P(B-A) ( A-B, B-A) =P(A)-P(A;B)+P(B)-P(A;B) = = P(A B)=;!; P(A;B) ;!;= P(A;B)=; 0; P(A'B)=P(A)+P(B)-P(A;B) P(A'B)=; 0;+;!;-; 0;=;@; 0 A, B 80 P(A)= P(A;B)=P(B)P(A B)= _ = P(A;B) P(B A)= = = P(A) A, B A={,, }, B={,,, } A;B={, } P(A;B)=,P(B)= P(A;B) P(A B)= = = ;!; P(B) 08 A A, B P(A)=;!0%;=;!;, P(A;B)=; 0;=;!; P(A;B) P(B A)= = =;@; ;@; P(A) 09 A, B 8 7 P(A)= =, P(A;B)= = P(A;B) P(B A)= = = P(A) A, B 0

47 00 ~ 0 P(A)=,P(B A)= = 7 P(A;B)=P(A)P(B A) P(A;B)= 7 P(A;B)= 9 0 A A, 00 C A P(A)= A 00 P(C A)= 9 P(A;C)=P(A)P(C A)= = A, B P(A)=, P(B A)= 9 8 P(A;B)=P(A)P(B A)= = A, B P(A)=,P(B A)= P(A;B)=P(A)P(B A) P(A;B)= = 0 p = 0,P(AÇ )=-P(A)=- =, P(B AÇ )= = P(AÇ ;B)=P(AÇ )P(B AÇ ) P(AÇ ;B)= = 0 p = 0 p +p = + = p 0% p 0% p +p 0% 0 A, B P(A;B) P(AÇ ;B) P(B)=P(A;B)+P(AÇ ;B) P(B)=P(A)P(B A)+P(AÇ )P(B AÇ ) P(B)= + = A A, B P(A)=P(A;B)+P(A;BÇ ) P(A)=P(B)P(A B)+P(BÇ )P(A BÇ ) 7 P(A)= + = 0 A, B P(A;B), P(AÇ ;B) P(B)=P(A;B)+P(AÇ ;B) =P(A)P(B A)+P(AÇ )P(B AÇ ) =0._0.+0.7_0. =0.+0. = E, A A, B B P(E)=P(E;A)+P(E;B) =P(A)P(E A)+P(B)P(E B) 0 0 P(E)= P(E)= 0 08 A A, B B, E P(A;E)=P(A)P(E A) =; 0º0;_;0%0;=; 0; P(B;E)=P(B)P(E B) =; 0º0;_;0#0;=;0(0;

48 RPM P(E)=P(A;E)+P(B;E) =; 0;+;0(0;=; 0ª0;, A P(A;E) 0 P(A E)= = =;!9); ;!9); P(E) A A, B B,, E P(E)=P(A;E)+P(B;E) P(E)=P(A)P(E A)+P(B)P(E B) C _ C C _ C P(E)= _ + _ C C 7 P(E)= + = 0 0 P(B;E) 0 9 P(B E)= = = P(E) P(A;E) 0 7 P(A E)= = = P(E) A={,, }, B={,, }, C={, } A;B=Δ, B;C={}, C;A={} P(A)=, P(B)=, P(A;B)=0 P(A;B)+P(A)P(B) A, B P(B)=, P(C)=, P(B;C)= P(B;C)=P(B)P(C) B, C P(C)=, P(A)=, P(C;A)= P(C;A)=P(C)P(A) C, A, P(A)=,P(B)=,P(C)=,P(D)= P(A;B)= =P(A)P(B) 00 A, B P(A)= = P(B)=P(A;B)+P(AÇ ;B) P(B)=P(A)P(B A)+P(AÇ )P(B AÇ ) P(B)= + P(B)= P(A;B) P(A B)= = = P(B) 0 A, B, E 7 7 P(A;E)=P(A)P(E A)= = P(B;E)=P(B)P(E B)= = 0 0 P(E)=P(A;E)+P(B;E) 7 9 P(E)= + = 0 0 P(B;C)= =P(B)P(C) P(C;D)=0+P(C)P(D) P(D;A)= =P(D)P(A) P(B;D)= =P(B)P(D) 0 A={,,, }, B={, } A;B={} P(A)=, P(B)=, P(A;B)= P(A;B)+P(A)P(B) A, B A={,,, }, C={,, } A;C={, } P(A)=, P(C)=, P(A;C)= P(A;C)=P(A)P(C) A, C A={,,, }, D={,,, } A;D={, } P(A)=, P(D)=, P(A;D)= P(A;D)+P(A)P(D) 08

49 0 ~ 0 A, D {,,, } 0 A, B P(A;B)=P(A)P(B) P(A'B)=P(A)+P(B)-P(A)P(B) = +P(B)-P(B) P(B)= 0 A, B P(A;B)=P(A)P(B)= = 0 P(A'B)=P(A)+P(B)-P(A;B) P(A'B)= P(A'B)= 0 07 P(A;BÇ )=P(A-B) =P(A'B)-P(B) = -P(B) P(B)= A, B P(A;B)=P(A)P(B) P(A'B)=P(A)+P(B)-P(A)P(B) =P(A)+ -P(A) P(A)= P(AÇ ;BÇ )=P((A'B)Ç )=-P(A'B) ;!;=-P(A'B) P(A'B)=;#; P(AÇ ;B)=P(A'B)-P(A) ;!;=;#;-P(A) P(A)=; ; A, B P(A;B)=P(A)P(B) P(A'B)=P(A)+P(B)-P(A)P(B) ;#;=; ;+P(B)-; ;P(B) 0 08 P(A'B)=P(A)+P(B)-P(A;B) =P(A)+P(B)- 8 8 P(A)+P(B)= A, B P(A;B)=P(A)P(B)= 8 P(A), P(B) t t -t+ =0, 8t -t+=0 8 8t -t+=0 (t-)(t-)=0 P(B)= ( P(A)>P(B)) 09 A A, B BA, B P(A;B)=P(A)P(B) P(A;B)= = ,, A, B, CA, B, C P(AÇ ;B;CÇ )=P(AÇ )P(B)P(CÇ ) P(AÇ ;B;CÇ )=(-0.8)_0._(-0.) P(AÇ ;B;CÇ )=0.0 0 A, B A, B A, B A, B P(A;B)=P(A)P(B) =0._0. =0. P(AÇ 'BÇ )=-P(A;B) =-0.= A, B 0% 0% P(B)=;7$; ;!; ;7$; 0 A, B, C A, B, CA, B, C 09

50 RPM AÇ, BÇ, CÇ P(AÇ ;BÇ ;CÇ )=P(AÇ )P(BÇ )P(CÇ ) ={-;$;}{-;#;}{-;!;} =; ; -P(AÇ ;BÇ ;CÇ )=-; ;=;@$; A, B, C A, B, CA, B, C A B P(A;B;CÇ )=P(A)P(B)P(CÇ ) =;@;_;!;_{-;@;}=;!; B C P(AÇ ;B;C)=P(AÇ )P(B)P(C) 0 AAÇ P(AÇ )= Cº{ } { } 8 = 8 7 P(A)=-P(AÇ )=- = 07 ;#;, ;@;, A, B P(A)= C {;#;} {;@;} =;@!^; P(B)= C {;#;} {;@;} =; ;, ;@!^;+; ;=;@(&; 7 ;@(&; ={-;@;}_;!;_;@;=; ; C A P(A;BÇ ;C)=P(A)P(BÇ )P(C) =;@;_{-;!;}_;@;=; ;,, ;!;+; ;+; ;=;@; ;@$; ;@; 0 x (-x) x-(-x)= x= C { } { } 0 = p=, q=0 p+q=8 0 ;!;, C { } { } = C { } { } = , ;!; ºCº{;!;} {;!;} =-;0 ; =;!0)@#; 09 -[ Cº{ } { } + C { } { } ]= 00 A C { } { } = 8 -;8 ;=;8*); ;8*); 0 C { } { } = 7 C { } { } =, 00

51 0 ~ 0 + = 7 7 7, ; ;+;8!;=; ; ; ; 0 ;!;, A, C {;!;} {;@;} =;8 ; 0 ;@; C {;!;} {;!;} =;!; ;!; C {;!;} {;!;} =;8!;, ;!;+;8!;=;8#; ;8#; 0% 0% 0% 0 ;!; ;!;, ;!; C {;!;} {;!;} =;8#; ;!;_;8#;=; ;, ;!; C {;!;} {;!;} =;!; ;!;_;!;=;8!; 0 P(A;B)=P(A)P(B) P(A;B) P(A)P(B) P(A B)= = =P(A) P(B) P(B) P(A;B) P(A)P(B) P(B A)= = =P(B) P(A) P(A) P(A B)+P(B A) () P(A;B)=0 P(A;B) 0 P(B A)= = =0 () P(A) P(A) P(A;B) P(A) P(B A)= = = () P(A) P(A) 0 P(AÇ ;BÇ )=P((A'B)Ç ) P(AÇ ;BÇ )=- P(A'B) P(AÇ ;BÇ )=-{P(A)+P(B)-P(A;B)} P(AÇ ;BÇ )=-{P(A)+P(B)- P(A)P(B) } P(AÇ ;BÇ )={-P(A)}{-P(B)} P(AÇ ;BÇ )=P(AÇ )P(BÇ ) 07 P(A;B)=0 P(A;B)=0+P(A)P(B) A, B() P(A;B)=P(A)P(B)+0 A, B () P(A;B)=P(A)P(B) P(AÇ ;B)=P(B)-P(A;B) =P(B)-P(A)P(B) ={-P(A)}P(B) =P(AÇ )P(B) AÇ, B() 08 P(A;B)=P(A)P(B A)=0._0.=0. P(A;B) P(B)= P(A B) 0. P(B)= = P(A;B)=P(B)P(A B) P(A;B)= = P(A'B)=P(A)+P(B)-P(A;B) P(A'B)= + - = 0

52 RPM 00 A, B P(A)=, P(B A)= P(A;B)=P(A)P(B A) P(A;B)= = 0 0 A, B A, B P(A;BÇ )=0., P(A'B)=0.8 P(B)=P(A'B)-P(A;BÇ )=0. A, B P(A;B)=P(A)P(B) P(A'B)=P(A)+P(B)-P(A)P(B) 0.8=P(A)+0.-0.P(A) P(A)=0.7 0 P(AÇ ;BÇ )=P((A'B)Ç ) P(AÇ ;BÇ )=-P(A'B) P(AÇ ;BÇ )= P(A'B)= P(A;B)=P(A)+P(B)-P(A'B) P(A;B)= +P(B)- P(A;B)=P(B)- P(A;B) P(A B)= P(B) P(B)- P(A B)= = P(B) P(B)- = P(B) P(B)= 0 A={,,, } P(A)=;$;=;@; B={,, }A;B={} P(A)=;@;, P(B)=;#;=;!;, P(A;B)=;!; P(A;B)+P(A)P(B) B={,, }A;B={, } P(A)=;@;, P(B)=;!;, P(A;B)=;@;=;!; P(A;B)=P(A)P(B) 0 B={,, } A;B={,, } P(A)=;@;, P(B)=;!;, P(A;B)=;!; P(A;B)+P(A)P(B) B={,,,, }A;B={,, } P(A)=;@;, P(B)=;%;, P(A;B)=;!; P(A;B)+P(A)P(B) B={,,,, } A;B={,, } P(A)=;@;, P(B)=;%;, P(A;B)=;!; P(A;B)+P(A)P(B) {,,, } 0 = A A={(, ), (, ), (, ), (, ), (, )} B B={(, )} A;B={(, )} P(A;B) P(B A)= P(A) P(B A)= = 0 A={,, }, B={,, }, C={, } A;B={}, B;C={}, A;C={} P(A)=, P(B)=, P(A;B)= P(A;B)+P(A)P(B) A, B P(B)=, P(C)=, P(B;C)= P(B;C)=P(B)P(C) B, C P(A)=, P(C)=, P(A;C)= P(A;C)=P(A)P(C) A, C, 0 A={,, }, B={,,, }, C={, }, D={,,, } A;B={, }, A;C={}, B;D={, } P(A)=,P(B)=,P(A;B)= 0

53 0 ~ 07 P(A;B)=P(A)P(B) A, B P(A)=,P(C)=,P(A;C)= P(A;C)=P(A)P(C) A, C P(B)=,P(D)=,P(B;D)= P(B;D)+P(B)P(D) B, D,, 07 A E,, F C _ C C _ C 7 P(F)= _ + _ = C C 0 C _ C P(E;F)= _ = C P(E;F) 8 P(E F)= = = P(F) A A, B B, C C, E P(A)=0., P(B)=0. P(C)=-{P(A)+P(B)}=0. P(A;E)=P(A)P(E A)=0._0.00=0.000 P(B;E)=P(B)P(E B)=0._0.00=0.00 P(C;E)=P(C)P(E C)=0._0.00=0.000 P(E)= P(E)=0.00 P(C;E) P(C E)= P(E) P(C E)= 0.00 P(C E)= 8 7 P(A'B)=P(A)+P(B)-P(A)P(B) P(A'B)= + - = P((A;BÇ )'(AÇ ;B)) =P(A'B)-P(A;B) = - = 070 p= C { } { } 0 = fi p 0 log =log { }=log 0 fi 0 fi log =log fi =- - º 07 P(r)= ºC { } { } ºC {} fi {} fi P() = = P() ºC {} fl {} 07 C { } { } 0 = 0 C { } fi { } = = A, B 8 P(A)=,P(A;B)= 0 0 P(A;B) P(B A)= P(A) 8 0 P(B A)= = (A;BÇ )'(AÇ ;B)=(A'B)-(A;B) P((A;BÇ )'(AÇ ;B))=P((A'B)-(A;B)) P((A;BÇ )'(AÇ ;B))=P(A'B)-P(A;B) A, B P(A;B)=P(A)P(B)= = 07 A={,,, }, B={,, } P(A)=;@;, P(B)=;!; A;B={, } P(A;B)=;!; P(A;B)=P(A)P(B) A, B() 0

54 RPM AÇ ={, } AÇ ;B={} P(AÇ )=;!;, P(AÇ ;B)=;!; P(AÇ ;B)=P(AÇ )P(B) AÇ,B() BÇ ={,, } A;BÇ ={, } P(BÇ )=;!;, P(A;BÇ )=;!; P(A;BÇ )=P(A)P(BÇ ) A, BÇ (),, 07 E, A P(A;E)=P(A)P(E A)= = 8 P(AÇ ;E)=P(AÇ )P(E AÇ )= = 8 P(E)=P(A;E)+P(AÇ ;E)= + = 8 07 _ C { } { } = _ C { } { } =, + = A A C { } { } 8 = 7 A A C { } { } = 9, = () S={,, }, A={, }, B={, } P(A'B)= B A () A, BP(A;B)=P(A)P(B) P(AÇ ;B)=P(B)-P(A;B) =P(B)-P(A)P(B) ={-P(A)} P(B) =P(AÇ )P(B) () A, B P(A;B)=0 P(A'B)=P(A)+P(B) P(S)= () A,B A;B=A P(A;B) P(A) P(B A)= = = () P(A) P(A) A, B A;B=Δ P(A;B) P(Δ) P(B A)= = =0 () P(A) P(A) A, BP(A;B)=P(A)P(B) P(A)+0, P(B)+0 P(A;B)+0 A, B(),,,,,, 079 P(A BÇ )=P(A)A, BÇ () P(A;B)=P(A)P(B) P(AÇ ;B)=P(B)-P(A;B) =P(B)-P(A)P(B) =P(B){-P(A)} =P(B)P(AÇ ) AÇ,B() P(AÇ ;BÇ )=P((A'B)Ç ) =-P(A'B) =-{P(A)+P(B)-P(A;B)} =-{P(A)+P(B)-P(A)P(B)} ={-P(A)}{-P(B)} =P(AÇ )P(BÇ ) AÇ,BÇ (),, () 0 a-, 0 -a a P(A;B)=P(A)P(B) =(a-)(-a) =-8a +a- P(A;B)=-8{a- } + 8 8,, P(A;B) a=,

55 08 ~ a, b a+b=, a-b= a=, b= C { } { } 0 = 0 08 P(AÇ ;BÇ )=P((A'B)Ç ) =-P(A'B) P(A'B)= =-P(A'B) P(AÇ ;B)=P(B-A)=P(A'B)-P(A) = -P(A) P(A)= A, B P(A;B)=P(A)P(B) P(A'B)=P(A)+P(B)-P(A)P(B) = +P(B)-P(B) P(B)= 7 P(A'B) 0% P(A) 0% P(B) 0% 08 A, B P(A;B)=P(A)P(B A) = = 0 9 P(AÇ ;B)=P(AÇ )P(B AÇ ) 7 7 = = P(B)=P(A;B)+P(AÇ ;B) 7 P(B)= + = A, B 0% P(A;B) 0% P(AÇ ;B) 0% P(B) 0% 08 C, D P(C)=, P(C;D)= 0 0 P(C;D) 0 P(D C)= = = P(C) 7 0 C, D 0% P(C), P(C;D) 70% P(D C) 0% 08 A, B = 9 = 7,, 9 P(A)= + + = P(A;B) 9 P(B A)= = = P(A)

56 RPM 0% 0% 0% 0% 08 f(p)= C p (-p)=p (-p) f(p) p (-p) = =p(-p) p p =-p +p=-{p- } + f(p) p=, p 087 a, b, c, d A, B, C, D a, c P(A;C)=P(A)P(C)=0._0.=0.08 b, d P(B;D)=P(B)P(D)=0._0.=0. a, b, c, d P(A;B;C;D)=P(A)P(B)P(C)P(D) =0._0._0._0.=0.0,, P Q = x= x= 089, ;!;, ;!; x, y, x+y= yy, xx, y y A x+y= yy, x=, y= C {;!;} {;!;} =;!; ;!; 088 A B A, B E P(A;E)=P(A)P(E A) =;!0); ;0#0;=;0!0; P(B;E)=P(B)P(E B) 0 x x = _ = A, B P(E)=P(A;E)+P(B;E) x P(E)= P(E)= +x 00 0, A ; ; P(A;E) 00 P(A E)= = = = P(E) +x +x 00 0

57 0 09 ~ 07 = p= n=00, p= P(X=0 X=)=P(X=0)+P(X=) =0.+0.= P(Xæ)=P(X=)+P(X=) =0.+0.= X0,, P(X=0)=,P(X=)=,P(X=)= X X 0 P(X=x) 09 E(X)=_ +_ +_ +_ = V(X)= _ + _ + _ + _ 8 8 V(X)=-{ } = ' 09 r(x)=" V(X)= 097 E(Y)=E(X+)=E(X)+=_+= V(Y)=V(X+)= V(X)=_ =, 098 E(Y)=E(X-)=E(X)-=_-= V(Y)=V(X-)= V(X)=_ = ', n=00,,,, 000 E(X)=_ = 00 V(X)= = ' 00 r(x)=" V(X)= P(0 X ) y=f(x) x x= P(0 X ) =;!; ;8#;=;ª; ;ª; 00, N(, ) N(, ) 00 E(Y)=E(X-)=E(X)-=_0-=9 r(y)=r(x-)= r(x)=_= E(Y)=9, r(y)= 007 P(Zæ.)=P(Zæ0)-P(0 Z.) =0.-0. = P(Z -0.)=P(Zæ0.) =P(Zæ0)-P(0 Z 0.) = = X 8, X-8 X-8 Z= Z= 00 P(X=)+P(X=)+y+P(X=9) k k = + +y+ k 9 8 ' y y=f(x) 8 O x 07

58 RPM =k[{-;!;}+{;!;-;!;}+y+{;8!;-;9!;}] =k{-;9!;}=;9*;k= k=;8(; 9 P(X=9)= = , X X 0,,,, ªC x C x _ C x X 0 P(X=)+P(X=)+P(X=)+P(X=) =k+k+9k+k=0k= k=; 0; k = k('x-'ƒx+) 'x+'ƒx+ ('x+'ƒx+)('x-'ƒx+) =k('ƒx+-'x) k{('-)+('-')+('-')+y+('å-'å)} =k= k=;!; ; 0; ;!; 0 + +a+ = a= P(Xæa)=P{Xæ } 9 P(Xæa)=P(X=)+P(X=)+P(X=) 8 P(Xæa)= + + = a 0% P(Xæa) 80% 0 P(X=)+P(X=)+y+P(X=0) 0 =a log +a log +y+a log = 9 0 a log { `y` }= 9 a log 0= a = P(X=)=log 8 9 C x _ C x P(X=x)= (x=0,,, ) ªC X Cº_ C P(X=0)= = ªC C _ C P(X=)= = ªC C _ C P(X=)= = ªC C _ Cº P(X=)= = ªC 0 X X 0 0 P(X=x) P(Xæ) P(Xæ)=P(X=)+P(X=) P(Xæ)=; ;+; ;=;!&; C x _ C x P(X=x)= (x=0,,, ) ªC ;!&; 0 X X 0, 00, 000, 000X X P(X=x) P(Xæ00)=P(X=000)+P(X=000) 0 P(Xæ00)= + = = (, ), (, ) (, ), (, ), (, ) 08

59 07 ~ 07 (, ), (, ), (, ), (, ) P( X ) =P(X=)+P(X=)+P(X=) 9 = + + = = X -X+ 0 (X-)(X-) 0 X P(X -X+ 0)=P( X ) =P(X=)+P(X=) +P(X=) C C P(X=)= = C C C 8 P(X=)= = C C Cº P(X=)= = C 8 P( X )= + + = ;!; ;#$; 09 X X P(X=x) E(X)=0_ +00_ +00_ E(X)=() X0,, C P(X=0)= = C 0 C C P(X=)= = C 0 C P(X=)= = C 0 X 0 P(X=x) E(X)=0_; 0;+_; 0;+_; 0;=;^; ;^; 07 X0,,, Cº C P(X=0)= = C 7 C C P(X=)= = C 7 C Cº P(X=)= = C 7 X X 0 P(X=x) P(X=0)+P(X=)= + = P(X )= a= 7 08 E(X)=0_a+_;!;+_b=;#; b+;!;=;#; b=;!; a+;!;+b= a=; ; a+b=_; ;+_;!;= x, X 00 x- E(X)=00000_ +0000_ +0_ =00 x x x 0000=00x x= X=,,, P(X=)= = X=,,,,,,,,,,, P(X=)= _ + _ P(X=)= + = X=,,,,,,, P(X=)= =,, X 09

60 RPM 9 E(X)=_ +_ +_ = 0 a+b+c= yy E(X)= a+b+c= yy V(X)=E(X )-{E(X)} V(X)=;!; a+b+9c-=;!;,, a=;!;, b=;!;, c=;!; yy abc=;!; ;!; ;!;=; ; ; ; 0 V(X)=E(X )-{E(X)} E(X )=V(X)+{E(X)} =+9 =9 9 E(X)=_ +_ +_ = 0 0 V(X)=E(X )-{E(X)} 9 V(X)={ _ + _ + _ }-{ } V(X)= X P(X=x) 9 r(x)=" V(X)=Æ = 9 p+q= ; ;+;!;=;#; ;#; 8 0 E(X)= x x= x(x+)(x+) E(X)= 8 E(X)= { - } x= x+ x+ E(X)= [{ - }+{ - }+ E(X)= y+{ - }] E(X)= { - }= 0 0 E(Y)=E(aX+b)=aE(X)+b 0a+b= V(Y)=V(aX+b)=a V(X) a =0, a = a= ( a>0) b= 8 x= (x+)(x+) 8 a+b= E(X)=_ +_ +_ +_ = V(X)= _ + _ + _ + _ -{ } V(X)= r(x)=" V(X)=Æ = r(-x+)= - r(x)=_ = 0 p+;!;+q+; ;= p+q=;@; yy E(X)=;!;+q+; ;=q+;!; V(X)=;!;+q+;ª;-{q+;!;} = q-{q+;!;} =0, q -8q+=0 (q-) =0 q=;!; q=;!; p=; ; 9 ;#; 08 E(X-)=E(X)-=-= V(X-)=V(X)=8 V(X-)=E((X-) )-{E(X-)} E((X-) )=V(X-)+{E(X-)} =8+= X-00 a=e(y)=e{ } a= E(X)-= _0-= b=e(y )=V(Y)+{E(Y)} X-00 b=v{ }+ b={ } V(X)+= _8+=8 a+b=+8= E(X)=, E(X )=9 00

61 07 ~ 07 V(X)=E(X )-{E(X)} =9-= E(Y)=E(aX+b)=aE(X)+b =a+b=0 yy V(Y)=V(aX+b)=a V(X) =a = a= ( a>0) a= b= ;!;+a+a =, 8a +a-=0 (a+)(a-)=0 a=;!; ( a>0) X X P(X=x) E(X)=00_;!;+00_;!;+00_;!; E(X)=00 E(aX+0)=aE(X)+0 E(aX+0)=;!;_00+0 E(aX+0)=8 8 0 X0,,, Cº C P(X=0)= = C C C 8 P(X=)= = C C Cº P(X=)= = C X X 0 8 P(X=x) 8 E(X)=0_ +_ +_ = E(-X)=-E(X)+ E(-X)=- += 0 X,,, C C P(X=)= = C C C P(X=)= = C C Cº P(X=)= = C X X P(X=x) a 0% E(X) 0% E(aX+0) 0% E(X)=_ +_ +_ = E(Y)=E(X-)=E(X)- E(Y)=_-= 00 X 0,, X E(X)=0_ +_ +_ = 8 V(X)=0 _ + _ + _ -{ } 8 V(X)= 8 X 0 P(X=x) 8 V(X-)= V(X) V(X-)=_ =0 8 0 X0,,, Cº C P(X=0)= = C 0 C C P(X=)= = C 0 C Cº P(X=)= = C 0 X X 0 P(X=x) E(X)=0_ +_ +_ =

62 RPM V(X)=0 _ + _ + _ -{ } 9 = r(x)=" V(X)= r(y)=r(0x+)= 0 r(x)=0_ = 0, ; 0;, ;ª0; X B{, ; 0;} P(X ) P(X )=P(X=0)+P(X=) = Cº{; 0;} {;ª0;} fi + C {; 0;} {;ª0;} 9fi _9 97 = + = 0fi 0fi 0000 =-[ ºCº { } + ºC { } + ºC { } ] 0 =-{ + + } =- = 0 8 p+q=8+=9 9 07, X X B{, ;$;} X P(X=x)= C x {;$;} {;!;} (x=0,,, ) P(Xæ)=P(X=)+P(X=) P(X>)= C {;$;} {;!;} + C {;$;} {;!;} B{, ; 0;} P(X>)=;!!@; ;!!@; P(X=x)= C x {; 0;} {;ª0;} fi (x=0,,,,, ) X B{7, } E(X)=7_ =8 0 X P(X=x)= C x { }= C x { } fi fi V(X)=7 = r(x)=' = 8, P(X=x)= C x {;@;} {;!;} fi (x=0,,,,, ) X B{, ;@;} np=_;@;=;; ;); ;; ;); 0 B{n, ;!;} X P(X=x)=«C x {;!;} {;$;} «(x=0,,, y, n) P(X=0)=«Cº{;!;} {;$;} «={;$;} «{;$;} «=;!^;={;$;} n= X B{0, Æ P(X=x)= ºCÆ { } { } P(X=x)= ºCÆ { } (x=0,,, y, 0) P(Xæ) =-{P(X=0)+P(X=)+P(X=)} } X 09 X P(X=x)= ººC x {;!;} {;!;} P(X=x)= ººC x {;!;} (x=0,,, y, 00) X B{00, ;!;} E(X)=00_;!;=0 V(X)=00_;!;_;!;= r(x)=' = E(X)+r(X)=0+= 00 X B{7, ;!;} E(X)=7_;!;= V(X)=7_;!;_;%;=0 0 x -x+0=0 a=-, b=0 a+b=

63 077 ~ X B(n, p) E(X)=0, V(X)= np=0 np(-p)= yy yy, 0(-p)= p=;!; E(X)=_;!;=;%; V(X)=_;!;_;!;=;%; E(aX+b)=aE(X)+b E(aX+b)=;%;a+b= yy p=;!; V(aX+b)=a V(X)=;%; a =0 ;!;n=0 n=00 a = a= ( a>0) yy b=-8 V(X)=;!%; np(-p)=;!%; yy ab=_(-8)=- P(X=n-)=P(X=n) «C«p«(-p)=«C«p«n(-p)=p p =;!%; p=;!; ( p>0) p=;!; yy 0 0 Y 0-Y X=Y-(0-Y)=Y-0 Y B{0, ;!;} E(Y)=0_;!;=0 ;#;n=;; ;; n= X B{, ;!;} E(X)=E(Y-0) =E(Y)-0 =_0-0=0 E(X)=_;!;=;%; 00 ;%; 0 ;#; 0 y=f(x) xx= ;!; a+_a= X B{0, ;#;} a=;@; ;@; E(X)=0_;#;=0 V(X)=0_;#;_;@;= V(X)=E(X )-{E(X)} E(X )=V(X)+{E(X)} =+900=9 07 y=f(x) x x= ;!; a= a=;!; ;!; y a O x 0, ;!; X B{80, ;!;}, E(X)=80_;!;=0, V(X)=80_;!;_;%;=, 08 f(x)=ax+a x, yx= y a a r(x)=" V(X)= E(X-)-r(X-) =E(X)-- r(x) =_0--_ = 0 X B{, ;!;} ;!; (a+a)= a=;@; O ;@; 09, - x f(x)æ0 y=f(x) xx=-, x= _= x 0

64 RPM f(x)æ0 y=f(x) x ;!; = y=f(x) xx= ;!; = P{;!; X } =;!; -;!;_;!;_;!; =;8#; ;8#; 00 y=f(x) x x= ;!; k= y k y=f{x} k O x a 0% P{;!; X } 70% k=;8!; P( X )=;!; {;!;+;!;} P( X )=;#; 0 P(X k) =;!;_k_{-;k;+} =;#; y - k O k x 0 P(0 X ) y=f(x) xx= P(0 X ) ={;!; ;!;}+{_;!;} =;!;+;!;=;@; y y=f{x} O x k -k+=0, (k-)(k-)=0 k= ( 0<k<) 0 m, x=m B, C B, C P{-;!; X ;!;} y=f(x) x y y=f{x} 0 m, r x=-;!;, x=;!; P{-;!; X ;!;} =-_{;!;_;!;_;!;} =;#; ;@; ;#; 0 y=f(x) x ;!; a= a= P{;!; X }y=f(x) xx=;!;, x= - - O y O y=f{x} x x 0 X N(, )X x= P(t- X t+) t- t+ t- t+ x (t-)+(t+), = t=;; ª;; 07 x=a P(X -)=P(Xæ) -+ a= = V{ X}= { } V(X)= V(X)= ;; ª;; b= a+b=7 7 0

65 079 ~ P( X ) =P(0- X 0+) =P(m-r X m+r) =P(m X m+r) =_0.77 =0.9 P(Xæ)=P(Xæ0+) =P(Xæm+r) =0.-P(m X m+r) =0.-0. = P(m-r X m+r)=a P(m X m+r)=a P(m X m+r)=;a; P(m-r X m+r)=b P(m X m+r)=b P(m X m+r)=;b; P(m-r X m+r) =P(m-r X m)+p(m X m+r) =P(m X m+r)+p(m X m+r) =;A;+;B; = a+b 00 P(X k)=0.08 P(X m)-p(k X m) =0.-P(k X m) =0.08 P(k X m)=0.77 P(m X m+r)=0.77 P(m-r X m)=0.77 k=m-r=8-_= 0 X X N(00, 0 ) P(Xæ0)=P(Xæ00+_0) =P(Xæm+r) =0.-P(m X m+r) =0.-;!;P(m-r X m+r) =0.-;!;_0.9 = a+b 0 X, Y N(0, ), N(0, ) X-0 Y-0 Z =, ZÁ= Z, ZÁ N(0, ) P(0 X )=P(0 Y k) P{ Z } 0-0 k-0 =P{ ZÁ } k-0 P(0 Z )=P{0 ZÁ } k-0 = k-0= k= 0 P(Xæk)=0.<0. k> X- Z= Z N(0, ) P(Xæk)=0. k- k- P{Zæ }=0.-P{0 Z } =0. k-, P{0 Z }=0. k- = k=9 9 X Z 0% k 80% 0 A X N(m, r ), X-m Z= r 8-80 = 8- = 80- = X, Y N(, ), N(m, ) Z = X-, ZÁ= Y-m 0

66 RPM Z, ZÁ N(0, ) P( X 7)=P(m Y m+) - 7- P{ Z } m-m (m+)-m =P{ ZÁ } m+ P(- Z )=P{0 ZÁ } m+ P(0 Z )=P{0 ZÁ } m+ = m= 0 XX N(00, ) X-00 Z= Z N(0, ) -00 P(Xæ)=P{Zæ } P(Xæ)=P(Zæ)=0.-P(0 Z ) =0.-0.= XX N(, ) X- Z= Z N(0, ) P(0 X 80)=P{ Z } P(0 X 80)=P(- Z ) =P(- Z 0)+P(0 Z ) =P(0 Z )+P(0 Z ) = = _0.800=8() 8 08 X X N(0, ) X-0 Z= Z N(0, ) -0 P(X )=P{Z } =P(Z ) =P(Z 0)+P(0 Z ) =0.+0.= XX N(7, ) a P(Xæa)= = X-7 Z= Z N(0, ) a-7 a-7 P{Zæ }=P(Zæ0)-P{0 Z } a-7 P{Zæ }=0.-P{0 Z }=0.07 a-7 P{0 Z }=0. a-7 =. a=8 8 8 X Z= Z N(0, ) P(0 X a)= a-0 P{ Z } a-0 =P{- Z } a-0 =P(- Z 0)+P{0 Z } a-0 =P(0 Z )+P{0 Z } a-0 =0.77+P{0 Z } =0.88 a-0, P{0 Z }=0. a-0 =, a-0= a= X- 07 Z= Z N(0, ) - P(X )=P{Z } P(X )=P(Z -) P(X )=P(Zæ) P(X )=0.-P(0 Z ), P( Z )=P(- Z ) =P(0 Z ) =0.8 0

67 08 ~ 08 P(0 Z )=0. P(X )=0.-0. = X N(m, r ) X-m P( X-m ar)=p{-a a} r =P(-a Z a) =P(0 Z a) =0.9 P(0 Z a)=0.77 P(0 Z )=0.77 a= k-0 07 P(Xæk)=P{Zæ } k-0 =P(Zæ0)-P{0 Z } k-0 =0.-P{0 Z } =0.08 k-0 P{0 Z }=0. P(0 Z.)=0. k-0 =. k=.. 07 X E(X)=0_ =90 V(X)=0 = X N(90, ) X-90 Z= Z N(0, ) P{9 X 0}=P{ Z } P{9 X 0}=P( Z.) =P(0 Z.)-P(0 Z ) = =0. 07 X E(X)=80_ =0 V(X)=80 = X N(0, ) X-0 Z= Z N(0, ) -0 P(X )=P{Z } P(X )=P(Z ) P(X )=P(Z 0)+P(0 Z ) P(X )=0.+0. P(X )= X E(X)=_ =80 V(X)= = X N(80, ) a=80, b= X-80 Z= Z N(0, ) P(8 X 80) =P{ Z } =P(- Z 0) =P(0 Z ) c= a+b+c=80++ = X E(X)=0_ =0 V(X)=0 =00 X N(0, 0 ) X-0 Z= Z N(0, ) 0 P(X=0)+P(X=)+y+P(X=70) =P(0 X 70) =P{ Z } 0 0 =P(- Z ) =P(- Z 0)+P(0 Z ) =P(0 Z )+P(0 Z ) = =

68 RPM 078 X B{70, } E(X)=70_;!;=0 V(X)=70_;!;_;%;=00 X N(0, 0 ) X-0 Z= Z N(0, ) 0 P(0 X 0) =P{ Z } 0 0 =P( Z ) =P(0 Z )-P(0 Z ) = = XX B{, ;!;} E(X)=_;!;= V(X)=_;!;_;!;= X N(, ) X- Z= Z N(0, ) 0- P(X 0)=P{Z } P(X 0)=P(Z -) =P(Zæ) =P(Zæ0)-P(0 Z ) = = XX B{00, } E(X)=00_;!;=0 V(X)=00_;!;_;!;= X N(0, ) X-0 Z= Z N(0, ) -0 P(Xæ)=P{Zæ } P(X )=P(Zæ) =P(Zæ0)-P(0 Z ) =0.-0.= X 00-0=0() P(Xæ0) X B(00, 0.) E(X)=00_0.=80 V(X)=00_0._0.8= X N(80, 8 ) X-80 Z= Z N(0, ) P(Xæ0)=P{Zæ } 8 =P(Zæ-.) =P(Z.) =P(Z 0)+P(0 Z.) = = XE(X), 0% V(X) P(Xæ0) 0% 08 X B(00, 0.0) E(X)=00_0.0=0 V(X)=00_0.0_0.98=9 X N(0, 7 ) X-0 Z= Z N(0, ) 7 P(k X 7) k =P{ Z } 7 7 k-0 =P{ Z } 7 k-0 =P{ Z 0}+P(0 Z ) 7 k-0 =P{0 Z - }+0. 7 =0.8 k-0 P{0 Z - }=0. 7 P(0 Z )=0. k-0 - = 7 k= 08

69 08 ~ XX B{00, ;!;} E(X)=00_;!;=0 V(X)=00_;!;_;$;= X N(0, ) X-0 Z= Z N(0, ) P(Xæa)=0.0 a-0 P{Zæ }=0.0 a-0 0.-P{0 Z }=0.0 a-0 P{0 Z }=0.8 P(0 Z )=0.8 a-0 = a= X B {8, ;!;} E(X)=8_;!;=8 V(X)=8_;!;_;@;= X N(8, 8 ) X-8 Z= Z N(0, ) 8 P(Xæa)=0.87 a-8 P{Zæ }= a-8 P(Zæ0)-P{0 Z }= a-8 0.-P{0 Z }= a-8 P{0 Z }=0. 8 P(0 Z )=0. a-8 8 a=0 = X N(0, ) a x= ººC x {;!;} {;$;} a = P(X=x) x= =P( X a) -0 a-0 =P{ Z } a-0 =P{- Z } a-0 =P(0 Z )+P{0 Z } a-0 =0.+P{0 Z } 0.8 a-0 P{0 Z } 0.8 P(0 Z )=0.8 a-0 P{0 Z } P(0 Z ) a-0 a 8 a XX X-8 N(8, 0 ) Z= Z 0 N(0, ) k P(Xæk)=; 0º0;=0.08 k-8 P{Zæ } 0 k-8 =P(Zæ0)-P{0 Z } 0 k-8 =0.-P{0 Z } 0 =0.08 k-8 P{0 Z }=0. 0 P(0 Z.)=0. k-8 =. 0 k= X B{00, ;!;} E(X)=00_;!;=0 V(X)=00_;!;_;$;= 087 XX X-80 N(80, 0 ) Z= 0 Z N(0, ) k 09

70 RPM P(Xæk)=0. k-80 P{Zæ }=0. 0 k P{0 Z }=0. 0 k-80 P{0 Z }=0.9 0 P(0 Z.)=0.9 k-80 0 k=9. = XX N(0, 0 ) a P(Xæa)= =0. 00 X-0 Z= Z N(0, ) 0 a-0 a-0 P{Zæ }=P(Zæ0)-P{0 Z } 0 0 a-0 P{Zæ }=0.-P{0 Z }=0. 0 a-0 P{0 Z }=0. 0 a-0 = 0 a= E(X+)=E(X)+= E(X)= V(X)= V(X)= V(X)=9 E(X )=V(X)+{E(X)} =9+ = 090 ;!;+a+;!;= a=;!; X +X-<0 (X+)(X-)<0 -<X< P(X +X-<0)=P(X=-)+P(X=0) P(X +X-<0)=;!;+;!;=;@; 09 a a+ +a = a +a-=0 (a-)(a+)=0 a= ( a>0) P(X =)=P((X+)(X-)=0) =P(X=- X=) =P(X=-)+P(X=) = + = 09 X N(, ) X- Z= Z N(0, ) Y N(0, ) k- P(Xæk)=P{Zæ }=P(Yæk) k- =k k=- 09 X E(X)=(-)_;!;+_;!;+_;!;=;#; E(X )=(-) _;!;+ _;!;+ _;!;=;; ;; V(X)=E(X )-{E(X)} =;; ;;-{;#;} =;$#; V(Y)=V(X+)= V(X) V(Y)=_;$#;= 09 P(k- X k+) k- k+ 8 (k-)+(k+) =8, k= k=;; ;; ;; ;; x f(x)æ0 y=f(x) x y=f(x) 070

71 08 ~ x ººC x {;@;} {;#;} 00 = x P(X=x) x=0 x=0 =E(X ) =V(X)+{E(X)} =00_;@;_;#;+{00_;@;} f(x)=;!;x- P{ X ;%;}=;!;_{;%;-}_;!; P{<X<;%;}=;!;_;!;_;!; P{<X<;%;}=; ; y O x = 098 X N(m, r ), X-m Z= r 8-8 = 8-78 = 7-8 = 7-7 =,,,,,, 00 X B{0, ;$;} P(X=x)= ºC x {;$;} {;!;} (x=0,,, y, 0) P(X )=P(X=0)+P(X=) = ºCº{;$;} {;!;} + ºC {;$;} {;!;} ={;!;} +0_;$;_{;!;} ={;!;} +0{;!;} ={;!;} k{;!;} ={;!;} k= 099 X B{80, ;!;} E(X)=80_;!;=0 V(X)=80_;!;_;#;= V(X)=E(X )-{E(X)} E(X )=V(X)+{E(X)} =+0 = 000 X P(X=r)= C {;!;} {;#;} fl (r=0,,, y, ) X B{, ;!;} E(X)=_;!;= r(x)=æ _;!; _;#; =' E(X)_r(X)=' 00 y=f(x) x x=, x= ;!; (k-+k-)= k=;!; 00 E(X)=0, V(X)=0 Y=X- E(Y)=E(X-) =E(X)- = 0- =99 V(Y)=V(X-)=V(X) =_00=00=0 YN(99, 0 ) Y-99 Z= Z N(0, ) P(Y 89)=P{Z } 0 =P(Z -0.) =P(Zæ0.) =P(Zæ0)-P(0 Z 0.) = = E(X)=np= yy, E(X )=0 V(X)=E(X )-{E(X)} =0- =, np(-p)= yy, (-p)= p=;!; 07

72 RPM p=;!; n=8 E(X)=80_;%;=0 00 XX N(8, 0 ) X-8 Z= Z N(0, ) P(Xæ0)=P{Zæ } 0 =P(Zæ0.) =P(Zæ0)-P(0 Z 0.) =0.-0. = _0.8=() 00 XX B{, ;!;} E(X)=_;!;=7 V(X)=_;!;_;!;= X N(7, ) X-7 Z= Z N(0, ) -7 P(Xæ)=P{Zæ } P(Xæ)=P(Zæ-) P(Xæ)=P(Zæ0)+P(0 Z ) P(Xæ)=0.+0. P(Xæ)= XX N(89, ) X-89 Z= Z N(0, ) P(Xæ07)=P{Zæ } P(Xæ07)=P(Zæ.) P(Xæ07)=P(Zæ0)-P(0 Z.) P(Xæ07)=0.-0. P(Xæ07)=0.07 n=00_0.07= 008 X B{80, ;%;} V(X)=80_;%;_;!;= X N(0, ) X-0 Z= Z N(0, ) 0-0 P(Xæ0)=P{Zæ } P(Xæ0)=P(Zæ) P(Xæ0)=0.-P(0 Z ) = = x ;!;_(b+a)_b= ab+b = yy, P(a X b)=;!; ;!;_(b-a)_b=;!; b -ab=;!;, b =;%; b>0 b= yy 00 X N(0, ) X-0 Z= Z N(0, ) a-0 P(Xæa)=P{Zæ } a-0 P(X>a)=P{ Z 0}+0. P(X>a)=0.9 a-0 P{ Z 0}=0.9 P(-0. Z 0)=0.9 a-0 =-0. a= m n X B{n, ' } +m ' 07

73 08 ~ 087 X 0, E(X)=n =0yy +m V(X)=n {- }=yy +m +m - = +m 0 m= n ; 0;=0 n=00 n-m=00-=9 9 X-m 0 P{ æ} r X-m =-P{ } r X-m =-P{- } r =-P(-r X-m r) =-P(m-r X m+r) =-P(m X m+r)=b -b P(m X m+r)= yy P(m-r X m+r) =P(m X m+r)+p(m X m+r) =a yy, -b P(m X m+r)+ =a -b P(m X m+r)=a- P(Xæm+r) =0.-P(m X m+r) -b = -{a- } =-a- b -a- 0 +a+ +b= 0 0 a+b= yy X _ +_a+_ +_b= 0 0 a+b=yy b, a=, b= V(X)=E(X )-{E(X)} V(X)={ _ + _ + _ + _ }- 0 0 V(X)= a, b 0% X a, b 0% a, b 0% V(X) 0% 0 X B{00, ;!;} E(X)=00_;!;=0 V(X)=00_;!;_;$;= X N(0, ) X-0 Z= Z N(0, ) -0-0 P( X )=P{ Z } P( X )=P(-. Z.) P( X )=P(0 Z.) P( X )=_0. P( X )= X B{00, ;!;} 0% X N(0, ) 0% P( X ) 0% 0 X N(00, 0 ) X-00 Z= Z N(0, ) 0 P(0 X a)=

74 RPM 0-00 a-00 P(0 X a)=p{ Z } 0 0 a-00 =P{- Z } 0 a-00 =P(- Z 0)+P{0 Z } 0 a-00 =P(0 Z )+P{0 Z } 0 a-00 =0.77+P{0 Z } 0 =0.979 a-00 P{0 Z }= P(0 Z )=0.987 a-00 = 0 a=0 0 X Z 0% a 80% ;9*; n, p 0% P(X=n-)=8P(X=n) n, p 0% p, n 0% P(X -X+<0) 0% 07 X P(X=r)=ªºC {;!;} {;@;} (r=0,,, y, 90) X B{90, ;!;} E(X)=90_;!;=0, V(X)=90_;!;_;@;=0 E(X )=V(X)+{E(X)} =0+0 =90 90 (r -r)p(x=r) r=0 90 = r P(X=r)- rp(x=r) r=0 90 r=0 =E(X )-E(X) =90-0 = X B{0, ;!;} 0 X B(n, p) V(X)=np(-p)=;9*; yy, P(X=n-)=8P(X=n) «C«p«(-p)=8«C«p«(-p) np«(-p)=8p«n(-p)=8p yy, p =;9!; 0 p p=;!; yy n ;@;=;*; n= P(X -X+<0)=P(<X<) =P(X=)+P(X=) = C {;!;} {;@;} + C {;!;} {;@;} =;8#@; ;8#@; E(X)=0_;!;=0 V(X)=0_;!;_;!;=0 E(X )=V(X)+{E(X)} =0+0 =0 f(a)=e{(x-a) }=E(X )-ae(x)+a =0-a_0+a =(a-0) +0 a=0, X y=f(x) y=f(x) x=0 P( X 0) 0 0 x =P( X 0)+P(0 X )+P( X 0) =P(0 X )+P(0 X )+P( X 0) =P(0 X )+P( X 0) >P(0 X ) () X 0 y=f(x) x +a X 0+a y=f(x) y=f(x) 0 0 x +a 0+a 07

75 087 ~ 089 x() () a=0, P( X 0) >P( X 0) () 00 0 % 00 XX B{00, ;!;} E(X)=00_;!;=00 V(X)=00_;!;_;!;=00 y=f(x) 0 0 X N(00, 0 ) X-00 Z= Z N(0, ) 0 k P(X k)æ0.9 k-00 P{Z }æ0.9 0 k P{0 Z }æ0.9 0 k-00 P{0 Z }æ0. 0 P(0 Z.)=0. k-00 =. 0 k= x 0 0, _=, _= C = 0 X E(X )= E(X )=+8 80 E(X )= = V(X )=E(X )-{E(X )} V(X )= V(X )= V(X )= X 7 8 P(X =x ) 8 8 ' 0 r(x )=" V(çX Ω)=Æ = 0 m, r, n E(X )=m=0 r 9 V(X )= = = n 0 0 r ' r(x )= = = 'n ' ' 0 0 N(, ) X 9 N{, }, N{, } 9 N{, } 07