III

3

0 0 03 04 6 «P! «C = 34= 343 r! r!(-r)! 3 5 0 6 7 8 9 0 4 8 4 0 A p A r «C p (-p) -r ( r=0y) () {()_() } = 3 ( ) 4

P(X=x)E(X)V(X)r(X) H T S S={(TT)(TH)(HT)(HH)} T H H H Tyy(TT) Hyy(TH) Tyy(HT) Hyy(HH) X S (TT)(TH)(HT)(HH) X 0 X 0 X S X S R X X (T, T) (T, H) (H, T) (H, H) P(X=x) 0 :: 4 :: P(X=0)=;4!;P(X=)=;!;P(X=)=;4!; 5

X X X x x yx X p p yp x x yx p p yp X P(X=x i )=p i (i=y) X X 0 X x x x y x«p(x=x) P(X=x) p p p y p«y O x x x y x«x Xa b P(a X b) X P(a X b)= b x=a P(X=x) P(X=x i )=p i (i=y) 0 p i p i = i= P(X=x) = CÆ{;!;} {;!;} = CÆ{;!;} (x=0) X X P(X=x) X 0 P(X=x) ;4!; ;!; ;4!; 4 O x X P( X )=P(X=)+P(X=) P( X )=;!;+;4!;=;4#; 6

X P(- X ) ( a ) X - - 0 P(X=x) ;5!; a a 3a a 4 3 3 X X 7 3 C 4 3 x (3-x) C x _ C 3-x X X 03 X Cº_ C C _ C P(X=0)= = P(X=)= = C 35 C 35 C _ C 8 C _ Cº 4 P(X=)= = P(X=3)= = C 35 C 35 X X 0 3 P(X=x) ;3 5; ;3!5@; ;3!5*; ;3 5; X CÆ_ C Æ P(X=x)= (x=03) C P(Xæ)=P(X=)+P(X=3) 8 4 P(Xæ)= + = 35 35 35 35 X X P(3 X 7) 7

6 4 3 X X 00 50000 30000 4 3 0000 0 0 85 00 50000_+30000_4+0000_0+0_85 33333333=350 00 yy X X X X 50000 30000 0000 0 P(X=x) ;0!0; ;0$0; ; 0º0; ;!0*0%; 4 0 85 50000_ +30000_ +0000_ +0_ =350 00 00 00 00 X 8

X X x x y x«p(x=x) p p y p«e(x) E m Expectatio mea x p +x p +y+x«p«= X E(X) m i= x p X X E(X)=x p +x p +y+x«p«= x p i= X X X X 3 4 5 6 P(X=x) ;6!; ;6!; ;6!; ;6!; ;6!; ;6!; X E(X)=_ +_ +3_ +4_ +5_ +6_ 6 6 6 6 6 6 E(X)= 6 =;&; ;&; 3 X X 3 9

X XE(X) m X x x x y x«p(x=x) p p p y p«x E(X)=m (X-m) (x -m) p V(X) V Variace r(x) r Stadard deviatio ()S (Sigma) x p =m p = i= i= X-m E((X-m) )=(x -m) p +(x -m) p +y+(x«-m) p«e((x-m) )= (x -m) p X V(X) øπv(x) X r(x) r(x)=øπv(x) XV(X) V(X)= (x -m) p V(X)= x i p i -m x i p i +m p V(X)= V(X)= i= i= i= i= i= x i p i -m +m x i p i -m V(X)=E(X )-{E(X)} i= i= X X P(X=x )=p (i=3y) E(X)=mX V(X)=E((X-m) ) =E(X )-{E(X)} r(x)=øπv(x) 0

X X X 0 3 P(X=x) ;3!; ;4!; ;4!; ;6!; 3 3 X X X P(X=x)= CÆ_ C Æ C (x=0) X X 0 P(X=x) ; 0; ; 0; ; 0; X 6 3 6 E(X)=0_ +_ +_ = 0 0 0 5 X V(X)=E(X )-{E(X)} 6 3 6 V(X)=0 _ + _ + _ -{ } 9 = 0 0 0 5 5 9 3 r(x)='ƒv(x)=æ = 5 5 V(X)=E((X-m) ) V(X)={0-;5^;} _; 0;+{-;5^;} _; 0;+{-;5^;} _; 0;=;ª5; 9 3 r(x)='ƒv(x)=æ = 5 5 9 V(X)= r(x)= 3 5 5 6 6 3 6 X X

ax+b X Y=aX+b aba+0 X x x y x«p(x=x) p p y p«y =ax +b(i=y) P(Y=y )=P(X=x )=p Y Y y y y y«p(y=y) p p y p«y x p =E(X) i= p = i= E(Y)=E(aX+b)= E(Y)=a x i p +b p E(Y)=aE(X)+b i= i= i= (ax +b)p X m Y V(Y)= {y -E(Y)} p = {(ax +b)-(am+b)} p i= V(Y)= a (x -m) p =a (x -m) p i= V(Y)=a V(X) r(y)=øπv(y)=øπa V(X) r(y)= a r(x) i= i= ax+b ax+b(aba+0) E(aX+b)=aE(X)+b V(aX+b)=a V(X) r(ax+b)= a r(x)

X E(X)=0V(X)=4 X+ E(X+)=E(X)+=_0+= V(X+)= V(X)=4_4=6 r(x+)= r(x)=_'4=_=4 50 4 X Y=aX+b E(Y)=-5V(Y)=4 ab ( a>0) 3 X m r Z= E(Z)=0 r(z)= X-m r X X-m Z= r Z 0 E(X)=mr(X)=r X-m m E(Z)=E{ }=E{ X- } r r r m m m E(Z)= E(X)- = - =0 r r r r X-m m r(z)=r{ }=r{ X- } r r r r(z)= r(x)= r= r r E(Z)=0r(Z)= m r X T X-m T=0{ 3}+00 r 46 48 0 T 90 90 T 3

X X 0 P(X=x) ;4!; ;!; k k X 00 500 X X 3 X E(X)=0V(X)=9 3X+ 345 5 X X P( X ) X 4

B(p) 4 3 X 43 P(X=)= {;3!;} X X 0 3 4 P(X=x) C {;3!;} {;3@;} 3 3 6 3 ;3!;3 ;3@; X P(X=x)= C x {;3!;} x {;3@;} 4-x (x=034) A p q A X X 0y P(X=k)=«C p k q -k (k=0yp+q=) B(p) B Biomial distributio B(, p) X B(p) 5

B(p) X (p+q)«(p+q)«=«cºq +«C pq - +«C p q - +y+«c p k q -k +y+«c«p p+q=(p+q)«= X 0 y k y P(X=k) «Cºq««C pq - «C p q - y «C k p k q -k y «C«p«k=0 k=0 «C p q -k «C p q -k = 0 X X B{0;!;} X B(p) 0 X 480 X 75 % 4 3 3 4 X X B{4 } 4 P(Xæ3)=P(X=3)+P(X=4) 3 = C { } { } 3 + C { } { } 4 4 4 4 08 8 = + = 56 56 89 56 89 56 6

9 0.3 5 9 X X 9 4 X B(p)X X B(3p) q=-p P(X=x)= CÆp q X 0 3 P(X=x) q 3pq 3p q p XE(X)V(X) r(x) E(X)=0_q +_3pq +_3p q+3_p E(X)=3p(p+q) =3p V(X)=0 _q + _3pq + _3p q+3 _p -(3p) V(X)=3p(p+q)(3p+q)-(3p) =3pq r(x)='ƒ3pq B(p) X X B(p) X q=-p E(X)=p V(X)=pq r(x)='ƒpq 7

X B{3 } 4 3 E(X)=3_ =8V(X)=3 =6r(X)='6 4 4 4 80 X X % 400 X X 6 4 00 X X B(, p) X X X 6 X X 6 X B{ } 6 X 5 P(X=k)=«C { } { } «k=03y 6 6 =03050 P(X=k) 8

B{ 6 } X - <0. X 6 =03050 0. 6 4 5 <X< 5 X P{ - <0.} =0 6 8 X 3 <X< 3 =0P{ - <0.}=P(X=)+P(X=) 0 6 X= =30P{ - <0.}=0.330+0.907=0.637 =30 <X<8 X =30P{ - <0.}=P(X=3)+P(X=4)+y+P(X=7) X=34567 30 6 =50 =30P{ - <0.}=0.368+0.847+y+0.098=0.7835 0 40 3 <X< 3 X =50P{ - <0.}=P(X=4)+P(X=5)+y+P(X=3) X=45y3 50 6 =30P{ - <0.}=0.0405+0.0745+y+0.039=0.9455 X P{ - <0.} 6 0. 0. 0.00.00y Ap A X p X 9

Ap A X h P{ X -p <h} X X A A P(A) X X B{30 } B{50 } 3 5 X X 30 X+3 0 60 63 (0.9fl =0.006 0.9fl =0.0050.9fl =0.003 ) 30

X B(p)X X P(X=k) 0_P(X=0)=0 P(X=k)=«C k p q«(p+q=k=0y) E(X)= kp(x=k)= k «C k p q«yy! (-)! k C k =k_ =_ = - C k!(-k)! (k-)!{(-)-(k-)}! k- E(X)= «C k- p q«e(x)=p «C k p q (-)-( -) =p(p+q)«=p E(X )= k C k p q - = {k(k-)+k} C k p q - E(X )= k(k-) C k p q - + k C k p q - E(X )= k=0 k= k= k= k= k= k(k-) C k p q - +E(X) k(k-) C k p q - =(-)p -C k- p - q - k= k= k= k= k(k-) C k p q - =(-)p -C k- p - q - k(k-) C k p q - =(-)p (p+q) - =(-)p E(X )=(-)p +p V(X) V(X)=E(X )-{E(X)} =(-)p +p-(p) =p(-p)=pq X B(, p) X q=-p E(X)=pV(X)=pqr(X)='ƒpq k= 3

A A 80 (æ) 4.0 æ ~ 4.5 æ 8 0. 4.5 æ ~ 5.0 æ 4 5.0 æ ~ 5.5 æ 6 5.5 æ ~ 6.0 æ 0 0.5 6.0 æ ~ 6.5 æ 6 0. 6.5 æ ~ 7.0 æ 6 80 :::::::::::: 0.50 0.40 0.30 0.0 0.0 0.00 4 4.5 5 5.5 6 6.5 7 æ = _ = X 3

0 O æ O æ X X X a X b X f(x) f(x) X X f(x) f(x)æ0 f(x) x x=a y y=f(x) x=b 3P(a X b) f(x) x x=a x=b a a X b b O a a b P(a X b) b x X c P(X=c)=0 P(a X b) =P(a<X b) =P(a X<b) =P(a<X<b) X f(x)= y ;:; O 0.8.4 (0 x ) f(x)=;:; x P(0 X )=_ = P(0.8 X.4)= _(.4-0.8)= _0.6=0.3 3 X f(x)= (0 x 5) P( x k)= 5 5 k 33

X f(x)=kx (0 x 4) k P( X 3) y OAB 4k B f(x)=kx OAB= _4_4k=8k= A O 3 4 k= 8 P( X 3) 3 9 8 _3_ - = - = = 8 8 6 6 6 P( X 3)= x 8 X f(x)=a(x-)(- x ) a P(- X 0) X f(x)=k ( x 6) 5 0 k P{ X } 3 0 X X 6 34

N(mr )N(0) 00 30 30 0 0 0 0 0 60 65 70 75 80 85 90 95 (cm) 0 50 55 60 65 70 75 80 85 (kg) (Gauss, K. F. ; 777~855) x X mrr>0) f(x) (x-m) 5 f(x)= e r (- <x< ) ' pr X e.788y X mr 35

N(mr ) N Normal distributio m r N(m, r ) X N(mr ) x X a b P(a X b) y O a y=f(x) b x (x-m) 5 N(mr ) f(x)= e r ' pr x=m f(x)=::::e ::::;:::: (x-m) r pr x 3x x=m m x ' pr 4m r r 5r m y r=0.8 m=-3 y m=0 m=3 r= r= O m 4m x -3 O 3 x 5r X70 5 N(705 ) x=70 0 0 0 36

X N(mr ) Z Z= Z E(Z)=0V(Z)= m r X 0 Z X 0 X-m r N(0, ) Z f(z) z=0 Z f(z) f(z)= e -;;; z (- <z< ) ' p Z N(0) Z 0 a P(0 Z a) f(z) -:: f(z)=:::;;e z p P(0 Z a) O a z Z N(0) P(0 Z.85).8 0.05 P(0 Z.85)=0.4678 z 0.00 0.0 y 0.05 y 0.08 0.09 0.0.0000.0040 y.099 y.039.0359 0..0398.0438 y.0596 y.074.0753 y y y y y y y y.8.464.4649 y.4678 y.4699.4706 Z N(0) P(0 Z.45) 37

Z N(0) P(- Z.96) P(Z ) P(- Z 0) =P(0 Z ) P(- Z.96) =P(- Z 0)+P(0 Z.96) =P(0 Z )+P(0 Z.96) =0.343+0.4750 =0.863 P(Z )=P(Z 0)+P(0 Z ) P(Z )=0.5+0.477 P(Z )=0.977 f(z) - O.96 z f(z) O z 0.863 0.977 Z N(0) Z.58 -.58 Z.58 P( Z.58) P( Z ) X N(04 ) P(8 X 4) X N(mr ) X-m Z= r X-0 Z= Z 4 N(0) 8-0 X-0 4-0 P(8 X 4)=P{ } 4 4 4 P(8 X 4)=P(-0.5 Z ) P(8 X 4)=P(0 Z 0.5)+P(0 Z ) P(8 X 4)=0.95+0.343 P(8 X 4)=0.538 f(z) -0.5 O z 0.538 38

X N(608 ) P(5 X 68) P(X 7) X N(mr )Xm-rm+r X-m Z= - r P(m-r X m+r) =P(- Z )=P(0 Z ) =_0.343=0.686 P(m-r X m+r)=0.9544 P(m-3r X m+3r)=0.9974 X m m-3r m-r m m+r m+3r m-r m+r 68.6 % 95.44 % 99.74 % rr3r 68.6 %95.44 %99.74 % x X N(mr ) P( X-m <kr)=0.95 k 3 00 g 8g 0 g X X N(008 ) X-00 Z= N(0) 8 X-00 0-00 P(Xæ0)=P{ æ } 8 8 P(X 0)=P(Zæ.5)=0.5-P(0 Z.5) P(X 0)=0.5-0.3944=0.056 0.056 0.056 39

74 cm 6cm 68 cm 77 cm % 46 000 640 80 X X B(p) =03050 B{ } 6 y =0 0.3 y 0.3 =0 0. =30 =50 0. =30 =50 0. 0. O 5 0 5 0x O x B(p) ppq N(ppq) q=-p X B(p)X N(ppq) 40

pæ5 (-p)æ5 X B(p)X N(ppq) q=-p 4 70 00 40 70 X X B{70 } 6 5 m=70_ =0r=æ 70 =0 6 6 6 70 X N(00 ) X-0 Z= N(0) 0 00-0 40-0 P(00 X 40)=P{ Z } 0 0 P(00 X 40)=P(- Z )=P(0 Z ) P(00 X 40)=_0.477=0.9544 0.9544 % 0000 86 0.6 50 0 4

Z N(0) P(-.34<Z<.34) P(Z<-0.88) X N(804 ) P(7 X 84) P(8 X 86) 3 X B{00 } P(45 X 60) P P 00 P 35 80 P -3 - - O 3 733 (a+b) (Laplace P S 749~87) (de Moivre, A. ; 667~754) 4

. S R X. X X 3. A p q(q=-p) A X X 4. X X 5. X mr(r>0) f(x) f(x)= e - (x-m) 3 r (- <x< )X ' pr m r 6. 0 0 X P( X 3) X 3 4 P(X=x) ;6!; ;3!; a 4a 0 4 X X+5 03 X B(400.) E(X) r(x) 43

04 X f(x) ( 0 x 4) y k y=f(x) k P( X 3) O 4 x 05 0000 60 g 4g 0000 5 g 06 ab (ab) (x-a) +(y-b) =4 x y 0 0 4 3 6 4 8 X X 07 0. 00 30 08 60 0 33 % B B 44

833 (Quetelet, L. A. J. ; 796~874) ' 5 N(mr ) (%) A B C D E 7 % 4 % 38 % 4 % 7 % 00 % 45

0 0 03 X X X 3 4 P(X=x) ;4!; ;8#; ;4!; ;8!; E(X)= x i p i i= V(X)=E((X-m) ) V(X)=E(X )-{E(X)} r(x)=øπv(x) 3 80 3 X X X N(600 )P(50 X 75) X B(p) E(X)=pV(X)=pq r(x)='ƒpq (q=-p) X N(mr ) X-m Z= r N(0 ) 46

X S S 00 00 00 0 47

8 0 6 9 3 5 7 4 5 4 0 3 7 9 8 6 RAND() 0 =INT((RAND()( - +)+ ) 00 0 A =INT(RAND()00)+ Eter A AA0 3 3 P =3 =9 C =3 P =6 345 5 3 48

357 4 4 X X X 3 5 7 P(X=x) ;4!; ;4!; ;4!; ;4!; X m r r m=4r =5r='5 X X yx - X X yx«x S S X = (X +X +y+x«) S = {(X -X ) +(X -X ) +y+(x«-x ) } - S=øπS X X X X +X X = X X X = X +X X +X [X = 3 ] X X 3 5 7 3 4 3 3 4 5 5 3 4 5 6 7 4 5 6 7 X 3 4 5 6 7 P(X =x ) ; 6; ; 6; ; 6; ; 6; ; 6; ; 6; ; 6; 49

E(X ) V(X ) X 3 4 3 E(X )=_ +_ +3_ +4_ +5_ +6_ +7_ =4 6 6 6 6 6 6 6 3 4 3 V(X )={ _ + _ +3 _ +4 _ +5 _ 6 6 6 6 6 5 +6 _ +7 _ }-4 = 6 6 X m=4r =5 r E(X )=m, V(X )= 3X X X X = X +X +X 3 X ;3%; ;3&; 3 ;; 3 ;; ;; 3 ;; 5 ;; 3 ;; ;; 3ª;; 7 P(X =x ) ;6 4; ;6 4; ;6 4; ;6!4); ;6!4@; ;6!4@; ;6!4); ;6 4; ;6 4; ;6 4; 5 X E(X )=4 V(X )= 3 5 r E(X )=4=mV(X )= = 3 3 m r X X X yx«x X X yx«x E(X )=E(X )=y=e(x«)=m V(X )=V(X )=y=v(x«)=r E(aX i )=ae(x i ) V(aX i )=a V(X i ) X X yx V{ X i }= V(X i ) i= i= E(X )=E{ X i }= E(X i ) i= i= E(X )=m V(X )=V{ X i }= V(X i ) i= i= V(X )= r 50

X X r N{m 3 } æ30 X m r X E(X )=mv(x )= r(x )= r X N{m } X N{m r r } r 'ƒ 3 5 36 5 5 X E(X )=3V(X )= r(x )= 36 6 N(57 ) 5 X 40 g 0 g 5 36 g 4 g m=40r=0=5 X 0 E(X )=40r(X )= = ' 5 X N(40 ) Z= X -40 N(0 ) 36-40 4-40 P(36 X 4)=P{ Z } P(36 X 4)=P(- Z ) P(36 X 4)=P(0 Z )+P(0 Z ) P(36 X 4)=0.477+0.343=0.885 0.885 5

40 g 30 g 00 X P(47 X 46) P(X 44) X 4 X X 0 P(X=x) ;6!; ;3@; ;6!; 40 0 5 X X ZP(38 X 44)=P(a Z b) ab a < b X 000 50 X 995 =5=00=65 5

(pisto rig) 00 00. mm 0.4 mm m m N(mr ) X X yx«x N{m } X Z= X -m N(0) r 'ƒ P(-.96 Z.96)=0.95 r Pª-.96 X -m.96º=0.95 r 'ƒ r r P{X -.96 m X +.96 }=0.95 'ƒ 'ƒ 0.95 -.96 0.96 z 53

r r m X -.96 m X +.96 95 % 'ƒ 'ƒ X x x -.96 r 'ƒ m x +.96 r 'ƒ m 95 % P(-.58 Z.58)=0.99 m 99 % x -.58 r 'ƒ m x +.58 r 'ƒ X x x x m x m m x x x y x m 95 % 95 % x m x m N(mr ) x m 95 %99 % 95 % x -.96 99 % x -.58 r 'ƒ r 'ƒ m x +.96 r 'ƒ m x +.58 r 'ƒ 54

m g 0 g 00 80 g m 95 % =00x =80r=0 m 95 % 0 0 80-.96_ m 80+.96_ 'ƒ00 'ƒ00 80-3.9 m 80+3.9 76.08 m 83.9 76.08 m 83.9 m 99 % r r S S=æ {(X -X ) +(X -X ) +y +(X«-X ) } - 5 7 m 95 % 69.06 m 74.94 x =7r=5 m 95 % 5 5 7-.96_ m 7+.96_ ' ' 5 _.96_ =74.94-69.06=5.88 ' _.96_5 '= =0 5.88 00 00 55

8.4 m 95 % 7.9 8.89 4 00 6 m 95 % 0 00 80 m 95 % m 99 % r m m a % a m b b-a b-a b-a;!; 56

p^ 00 00 73394 4465 00 (http:kostat.go.kr) p Proportio 4465 73394 p p^ ^p X ^p ^p= X A p X ^p= X A 57

X B(p) B(p) X E(X)=pV(X)=pq (q=-p) ^p X E(^p)=E{ }= E(X) E(^p)= p=p X V(^p)=V{ }= V(X) V(^p)= pq= r(^p)=øπv(^p)=æ pq pq B(p) X pq N(p pq)(q=-p) E(^p)=p V(^p)= X pq ^p= N{p } Z= ^p-p æ pq N(0) pæ5(-p)æ5 ^p ^p N{p Z= ^p-p æ pq pq } N(0) q=-p A 80 % 00 ^p E(^p)=p=0.8 r(^p) 0.8_0. r(^p)=æ =0.04 00 58

90 % 400 ^p ^p 80 % 00 80 % 90 % 00 ^p E(^p)=p=0.8 pq 0.8_0. 0.6 V(^p)= = = =0.006 00 00 r(^p)=" V(^p)='ƒ0.006=0.04 ^p N(0.80.04 ) ^p-p ^p-0.8 ^p-0.8 Z= = = N(0) 0.04 æ pq æ 0.8_0. 00 0.8-0.8 0.9-0.8 P(0.8 ^p 0.9)=P{ Z } 0.04 0.04 P(0.8 ^p 0.9)=P(0 Z.5) P(0.8 ^p 0.9)=0.4938 0.4938 50 % 64 40 % 59

(Fisher, R. A. ; 890~96) p ^p pq ^p-p N{p } (q=-p) Z= æ pq N(0) ^p Z= ^p-p æ ^p^q pq^p^q(=-^p) N(0) ^p-p P(-.96 Z.96)=Pª-.96.96º=0.95 æ ^p^q ^p^q P{^p-.96æ p ^p+.96æ ^p^q }=0.95 p ^p-.96æ ^p^q p ^p+.96æ ^p^q 95 % ^p^q ^p-.96æ p ^p+.96æ ^p^q p 95 % pq P(-.58 Z.58)=0.99 p99 % ^p-.58æ ^p^q p ^p+.58æ ^p^q ^p p^ p^ p^ p^ p y p^ p^ p 60

p 95 % 95 % p p ^p p 95 %99 % ^q=-^p 95 % : ^p-.96æ 99 % : ^p-.58æ ^p^q ^p^q p ^p+.96æ ^p^q p ^p+.58æ ^p^q 400 30 p 95 % 30 ^p-p =400^p= =0.8 Z= 400 æ ^p^q p 95 % ^p-.96æ ^p^q 0.8_0. =0.8-.96æ 400 ^p+.96æ ^p^q =0.7608 0.8_0. =0.8+.96æ 400 =0.839 0.7608 p 0.839 0.7608 p 0.839 99 % 6

400 95 % 96 360 33 68 80 300 8 ^p 5 ^p ;!; p 95 % 400 ^p 0. p 95 % ^p-p 6

. m r X E(X )= V(X )= r(x )= X N{ }. N( ) x m 95 % x - m x + 3. ^p N{p } ^p-p Z= N(0) q=-p 4. ^p p 95 % ^p- p ^p+ ^q=-^p 0 3 4 X X X 0 3 5cm 3 00 7 cm 3 m 95 % 63

03 40 % 00 ^p 04 4000 0 00 4030 05 6 g m 95 % a m b b-a 4 06 A 300 8 ^p ^p p 95 % 0.70 p 0.799 300 8 64

00 5000 mg 80 mg 95 % 80 80 5000-.96_ m 5000+.96_ 'ƒ00 'ƒ00 4984.3 m 505.68 4984.3 mg 505.68 mg 4984.3 m 505.68 00 95 % 00 95 % 4984.3 m 505.68 65

0 5 5 X X 3 5 4 X 34 0 X E(X)=5 V(X)=5 E(aX+b)=50, V(aX+b)=45 ab E(aX+b) =ae(x)+b V(aX+b) =a V(X) 03 X P(X=r)= ººC {;5!;} {;5$;} (r=0y00) X X B(p) E(X)=p r(x)='ƒpq (q=-p) 04 X f(x)=ax+a(0 x ) x a P{0 X ;!;} 05 X N(6 ) t t -Xt+9=0 t -Xt+9=0 D 4 =X -9<0 66

06 7 3 X P(6 X 3) 07 0 4 8 XÚ XÚ E(XÚ ) V(X ) =E(X )-{E(X )} 08 000 g 00 g 7 XÚ P{XÚæ950+ }æ0.90 ' ( P(0 Z.8)=0.4) N(mr ) X X r N{m 4 } 09 400 00 p 95 % p 95 % ^p-.96æ ^p^q p ^p+.96æ ^p^q 0 9.5 kg/cm 00 x x x yx 00 00 x 00 x i i= x =;0!0; 00 x =3700(kg/cm ) i= m 95 % 67

X B(00) P(X=4) (S ) BINOM.DIST Numbers - s P(X=k) k4 Trials B(p) 0 Probability - s B(p) p0 Cumulative false 0.088080384 P(X=4)0.088080384 X B(400.4) P(X=8) X N(405 ) NORM.DIST P(35 X 45) 68

m 4 36 0 m 95 % CONFIDENCE.NORM Alpha -()-095=005 Stadard - dev r4 Size 36 30664656 m 95 % 0-.30664656 m 0+.30664656 8.693357344 m.30664656 3 4 0 00 8 m 95 % 6 00 80 m 99 % 69

IWC 8 IWC 986 009 700 (95 % 3.7 % 67.9 % 5.4 % IWC(Iteratioal Whalig Commissio) 70067.9 % 95 % 3.7 % (67.9 3.7) % 70

(Digest) 936 40 57 % (LadoAM887~987) The America Istitute of Public Opiios (GallupG90 ~984) 6 % (Roosevelt, F. D. ; 88~945) 40 0 0 03 04 0 0 03 7