1( = @ 1( > 2( > 3( 4( > 2( 45 % @ @ > > > @ > > = > 1( 180 2( 162 3 ...
1( = @ 1( > 2( > 3( 4( > 2( 45 % @ @ > > > @ > > = > 1( 180 2( 162 3 ... 1( = @ 1( > 2( > 3( 4( > 2( 45 % @ @ > > > @ > > = > 1( 180 2( 162 3 ...
104a + b 15 + 25µ = E(x) = = = 202 2d − c 25 − 20P(c < x < d) = = =b − a 25 −15510=12. 3 (21. 4 (22. . 3 (23E (ax + b) = aE(x) + b = aµ + bV (ax + b) = a2V(x) = a2δ2P(XY> 0 ) = P(X > 0,Y> 0)+ P(X < 0,Y< 0). 1 (24. 1 (25: P(XY> 0 ) = P(X > 0)P(Y> 0)+ P(X < 0)P(Y< 0): 1 1 1 1 1 1P(XY > 0 ) = × + × = + =2 2 2 2 4 412x, y X 2 . 2 (26X ~ X2(n) ⇒ E(X) =P(X < 300)=Z2~ χ2( 1xP(n, V(X)= 2n− µ 300−300< ) = P(Z < 0)=δ 60012: X 2 ) Z . 3 (27: V(Z) = E(Z2) − Z2(Z) ⇒ 1 = E(Z2) −0⇒E(Z2) = 1V(Z2) = E(Z4) − E2(Z2) ⇒ 2 = E(Z4) −1⇒E(Z4) = 3E(z2) = 1,Var(z2) = 2
105 f (x) =1b − a0a < x
- 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 and 30: 71Var(y) = a2Var(x) = ( −2)2× 1/
- Page 31 and 32: 73xy012f (y) ( (11 2 3 6 x-18 8
- 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: 103 . 2 (7. 3 (8. 2 (9. 4 (
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- 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.
104a + b 15 + 25µ = E(x) = = = 202 2d − c 25 − 20P(c < x < d) = = =b − a 25 −15510=12. 3 (21. 4 (22. . 3 (23E (ax + b) = aE(x) + b = aµ + bV (ax + b) = a2V(x) = a2δ2P(XY> 0 ) = P(X > 0,Y> 0)+ P(X < 0,Y< 0). 1 (24. 1 (25: P(XY> 0 ) = P(X > 0)P(Y> 0)+ P(X < 0)P(Y< 0): 1 1 1 1 1 1P(XY > 0 ) = × + × = + =2 2 2 2 4 412x, y X 2 . 2 (26X ~ X2(n) ⇒ E(X) =P(X < 300)=Z2~ χ2( 1xP(n, V(X)= 2n− µ 300−300< ) = P(Z < 0)=δ 60012: X 2 ) Z . 3 (27: V(Z) = E(Z2) − Z2(Z) ⇒ 1 = E(Z2) −0⇒E(Z2) = 1V(Z2) = E(Z4) − E2(Z2) ⇒ 2 = E(Z4) −1⇒E(Z4) = 3E(z2) = 1,Var(z2) = 2
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