Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig

Answers to Selected Exercises 731

10.9.90; [4f^2 (θ)]−^1.

10.9.14ŷLS=3.14 +. 028 x;
ŷW=0.214 +. 020 x.

Chapter 11

11.1.1 0 .45; 0. 55.

11.1.3[yτ^2 +μσ^2 /n]/(τ^2 +σ^2 /n).

11.1.4β(y+α)/(nβ+1).

11.1.6 n+αy 11 ++αα 21 +α 3 ;n+αy 12 ++αα 22 +α 3.

11.1.8(a)

(

θ−10+30 45 θ

) 2

+

( 1

45

) 2

30 θ(1−θ).

11.1.9^6

√

2 ,y 4 <1;^6

√

2 y 4 , 1 ≤y 4.

11.2.1(a) θ

(^22)
[θ^22 +(x 1 −θ 1 )^2 ][θ^22 +(x 2 −θ 1 )^2 ].
11.2.3(a) 76.84; (b) (76. 25 , 77 .43).
11.2.5(a)I(θ)=θ−^2 ;(d)χ^2 (2n).
11.2.8(a) beta(nx+1,n+1−nx).
11.3.1(a) LetU 1 andU 2 be iid
uniform(0,1):

1. DrawY=−log(1−U 1 )


2. DrawX=Y−log(1−U 2 ).

11.3.3(b)FX−^1 (u)=−log(1−

√

u),

0 <u< 1.

11.3.7(b)f(x|y)isab(n, y)pmf;
f(y|x)isabeta(x+α, n−x+β)
pdf.

11.4.1(b)β̂= 21 x;(d)θ̂=^1 x.

11.4.2(a)δ(y)=

R 1

0 [ 1 −aalogp]

(^2) py(1−p)n−ydp
R 1
0 [ 1 −aalogp]
(^2) py− (^1) (1−p)n−ydp.