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72Cov(x, y)P (x,y) =δ x δ y=Cov(x, y)⇒ Cov(x, y) = 1V(x + y) = V(x) + V(y) + 2Cov(x,y) = 3 + 3 + 2 = 8P = 0/ 8n = 5P (x,y)=Cov(x, y)δ x δ y3⎛5⎞P (X = 1 ) = ⎜ ⎟(0/8)(0/2)4= 0/0064⎝1⎠⇒ 0/5 =Cov(x, y)Cov(x, y)V(x − y) = V(x) + V(y) − 2Cov(x,y) = δ2+ δ2− δ2= δ2 x, yδδ⇒. 3 (17. 3 (18= 0/5δ2 . 1 (19F (x, y) =Fx (X)Fy (Y): . 2 (20[ − 1 )(y − 2)] = E(x −1)E(y− 2)= [ E(x) −1][ . E(y) − 2] = ( 6 −1)(3 − 2)= 5E (x. 3 (21 . 3 (22 1000 n = 0 / 71×1000 = 710:E(Y) = 0⇒E(ax + b) = aE(x) + b = 5a+ b = 0F = 0 / 23 + 0/48 = 0/71 1V(y) = 1⇒V(ax + b) = 1⇒a2V(x) = 1⇒4a2= 1⇒a = ±2155a+ b = 0⇒5×( ± ) + b = 0⇒b = ±22. 2 (23. 2 (24
73xy012f (y) ( (11 2 3 6 x-18 8 8 82 1 2 1 4 211 2 f (x) = = =108 4 8 4 8 488 8 y -1 12 1 4f (x)8 4 86 3 2 1f (y) = =1 1 2 58 4 8 4E(x) = ∑ xp(x) = 0×+ 1×+ 2×=4 4 4 4(3 1 −2E(y) = ∑ yp(y) = −1×+ 1×=4 4 41 2 3 1E(xy) = ∑ ∑ xyf (x, y) = −1×0×+ ( −1)× 1×+ ( −1)× 2×+ 1×× 0+1×1×0+x y8 8 8 81 6 31×2×= − = −8 8 43 2 5 − 2 1Cov(x, y) = E(xy) − E(x)E(y) = − − ( − )( ) = = −4 4 4 16 81 1 2 9E(x2) = ∑ x2f (x)= 0×+ 1×+ 4×=(4 4 4 49 5 11Var(x) = E(x2) − [ E(x) ]2= − ( )2=4 4 63 1E(y2) = ∑ y2f (y) == ( −1)2× + 1×= 14 423[ ]2 − 2Var(y) = E(y ) − E(y) = 1−( )2=4 411 3 1Var( 2 x + y) = 22Var(x) + Var(y) − 2×2×1×Cov(x, y)= 4×+ + 2×2×= 46 4 85 4 5 4 40 4P ( ) = × + × = =(210 9 10 9 90 9 X 1/1 -14 5P ( ) = 1 − =4 59 9P(x)4 59 9E(x) = ∑ XP(x) = 1 / 1×+ ( −1×) = −0/067 x9 92 25[ ]2 ⎡ 2 41 1 12 ⎤δ X P(x)E(x) / ( ) [ 0/067] 2x = ∑ − =⎢× + − × − − = 1/088x9 9⎥⎣⎦012
Page 1 and 2: 43 (4 (3 (1 (2 (1
Page 3 and 4: 45 20 100 (16( ) 150 -
Page 5 and 6: 47 (2 (4 14 . . (2.
Page 7 and 8: 49 . 2 (1α i= 360×
Page 9 and 10: 51 n 100= = 502 2n− Fi −1m =2
Page 11 and 12: 53fi= ( < < ) . (2( < < ) .
Page 13 and 14: 55P(AU B)2 1P(B) = , P(A) =3 372(4(
Page 15 and 16: 576! (44× ! 3!(3 . 3 ! × 2!
Page 17 and 18: 59 4 3 . 21 (1
Page 19 and 20: 611 81−= ⇒ k = 3 ⇒ µ − kδ
Page 21 and 22: 63 P ( ) = P( )3 4 3 6 1P ( )
Page 23 and 24: 65 4 1 33P(W 1 ) =7 3 2 4P(B1
Page 25 and 26: 67X = xP (X =x) (435 (4 E (
Page 27 and 28: 69 1000 δx= 2µx 770
Page 29: 71Var(y) = a2Var(x) = ( −2)2× 1/
Page 33 and 34: 75 a . 3 (8:
Page 35 and 36: 77 ⎛4⎞⎛66⎞⎛4⎞⎛66⎞
Page 37 and 38: 797(49 ( E(X) = λ)100−1−e λ(4
Page 39 and 40: 81 . . 3 (1λ x = δ
Page 41 and 42: 83E(x) = np = 43 / 2Var(x) = npq =
Page 43 and 44: 85e−λλxP(x) =X!P(X ≥ 2)= 1−
Page 45 and 46: 87f (x) =1µ = δ =λ . .
Page 47 and 48: 89 P( − a < z < a)0/921=2(4 6
Page 49 and 50: 9122− (4(399 1818(40/6587 (
Page 51 and 52: 93 1 3P ( −a< z < a) = 2 φ a
Page 53 and 54: 95P − PP(P < 0/6)= P(Z < ) = P(Z
Page 55 and 56: 97 X . δ = 2 µ =10 (1 (1
Page 57 and 58: 99. (4 n1 + n2−2 (3 X
Page 59 and 60: 101: P(X< 300): (4 E(Z4 )1(
Page 61 and 62: 103 . 2 (7. 3 (8. 2 (9. 4 (
Page 63 and 64: 105 f (x) =1b − a0a < x
Page 65 and 66: 107 (4 (3 (2H 1 :
Page 67 and 68: 1090/31250 (40/343 (3 . 100 0/
Page 69 and 70: 111 . H 0 H 0 . 3 (1
Page 71 and 72: 113 3 2 (4 Y = 3 +0/4X0〈r≤
Page 73 and 74: 115 (4( r = 100r′)X(3 Y,Y( B = B
Page 75 and 76: 117 . X y . r=1 .
Page 77 and 78: 11921212102121012121212121212121012
Page 79 and 80: 121 82-8383 60: ( ) 20:
Page 81 and 82:
123 13 (141Lnλ2(42Lnλ(31
Page 83 and 84:
125 . 4 (10 37374
Page 85 and 86:
127 84-85 60: ( ) 20: .
Page 87 and 88:
1291f (x) =θ (44X، 0< x < θ(4
Page 89 and 90:
131Cov(x, y)= E(xy) − E(x)E(y) =
Page 91 and 92:
133 711E(X / Y = 1)1520(4(4 f (x,
Page 93 and 94:
135 . 225 µ X (18%95
Page 95 and 96:
137 . 380 34-1 (40/75 (4n 2 n
Page 97 and 98:
139f (x / y) =fx (x) =fy (y) =3 x23
Page 99 and 100:
141x-2-10210y413-1-25 . 2 (23.
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