Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig

Answers to Selected Exercises 729

7.6.3(a) 0.8413; (b) 0.7702 (c) Our run

0.0584.

7.6.4(a) 49.4; (b) Our run: 4.405

7.6.6(a)

(n− 1

n

)Y(

1+nY− 1

)

;

(b)

(n− 1

n

)nX(

1+nn−X 1

)

;

(c)N

(

θ,θn

)

.

7.6.9 1 −e−^2 /X;1−

(

1 −^2 /nX

)n− 1

.

7.6.10(b)X;(c)X;(d)1/X.

7.7.3Yes.

7.7.5(a)Γ[(Γ[n−n/1)2]/2]

√

n− 1

2 S.

(b) Downloadbootse6.R

10.1837; Our run: 1.156828

7.7.6(b)Y^1 + 2 Yn;(n+1)(2(nY−n1)−Y^1 ).

7.7.7(a)K =(Γ((n−1)/2)/Γ(n/2))
×

√

((n−1)/2)

mvue = Φ−^1 (p)KS+x

(c) 59.727; Our run 3.291479.

7.7.9(a)n−^11

∑n

h=1(Xih−Xi)

×(Xjh−Xj);

(b)

∑n

i=1aiXi.

7.7.10

(∑

n

i=1xi,

∑n

i=1

1

xi

)

.

7.8.3Y 1 ,;

∑n

i=1(Yi−Y^1 )/n.

7.9.13(a) Γ(3n, 1 /θ),no;
(c) (3n−1)/Y;
(e) Beta(3, 3 n−3).

Chapter 8

8.1.4

∑ 10

i=1x

2

i≥^18 .3; yes; yes.

8.1.5

∏n

i=1xi≥c.

8.1.6 3

∑ 10

i=1x

2

i+2

∑ 10

i=1xi≥c.

8.1.7About 96; 76. 7.

8.1.8

∏n

i=1[xi(1−xi)]≥c.

8.1.9About 39; 15.

8.1.10 0 .08; 0. 875.

8.2.1(1−θ)^9 (1 + 9θ).

8.2.2 1 − 1615 θ 4 , 1 <θ.

8.2.3 1 −Φ

( 3 − 5 θ

2

)

.

8.2.4About 54; 5. 6.

8.2.7RejectH 0 ifx≥ 77. 564.

8.2.8About 27; rejectH 0 ifx≤ 24.

8.2.10Γ(n, θ);

RejectH 0 if

∑n

i=1xi≥c.

8.2.12(b) 326 ;(c) 321.

(d) reject ify=0;

ify= 1, reject with probability^15.

8.3.1(b)t=− 2. 2854 ,p=0.02393;

(c) (− 0. 5396 − 0 .0388).

8.3.5(d)n= 90.

8.3.678; 0.7608.

8.3.10UnderH 1 ,(θ 4 /θ 3 )Fhas

anF(n− 1 ,m−1) distribution.

8.3.12RejectH 0 if|y 3 −θ 0 |≥c.

8.3.14(a)

∏n

i=1(1−xi)≥c.

8.3.17(b)F=1.34;p=0.088.

8.4.1 5. 84 n− 32 .42; 5. 84 n+41. 62.

8.4.2 0. 04 n− 1 .66; 0. 04 n+1. 20.

8.4.4 0. 025 , 29. 7 ,− 29. 7.

8.5.5(9y− 20 x)/ 30 ≤c⇒(x, y)∈2nd.

8.5.7 2 w^21 +8w^22 ≥c⇒(w 1 ,w 2 )∈II.

Chapter 9

9.2.3 6. 39.

9.2.6(b)F=1.1433,p=0. 3451.

9.2.7 7. 875 > 4 .26; rejectH 0.

9.2.8 10. 224 > 4 .26; rejectH 0.