Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig

726 Answers to Selected Exercises

4.2.10c=

√

n

n+1;k=1.^50.

4.2.13ind=rep(0,numb);

for(i in 1:numb){if

(ci[i,1]*c[i,2]<0){ind[i]=1}}

4.2.14

( 5 x

24 ,

5 x

16

)

.

4.2.16 6765.

4.2.17(3. 19 , 3 .61).

4.2.18(b) (3. 625 , 29 .101).

4.2.21(− 3. 32 , 1 .72).

4.2.26135 or 136.

4.3.1(c) (0. 1637 , 0 .3642).

4.3.3(0. 4972 , 0 .6967).

4.3.4(c) (0. 197 , 1 .05).

4.4.2(a) 0.00697; (b) 0.0244; (c) 0.0625

4.4.5(a) 4, 23 , 67 , 99 ,301.

4.4.5 1 −(1−e−^3 )^4.

4.4.6(a)^18.

4.4.10Weibull.

4.4.11 165.

4.4.12pdf: (2z 1 )(4z^32 )(6z^53 ),
0 <zi< 1.

4.4.13 127.

4.4.17(a) 48y^53 y 4 , 0 <y 3 <y 4 <1;

(b)^6 y

35

y^64 ,^0 <y^3 <y^4 ;(c)

6

7 y^4.

4.4.18^14.

4.4.19 6 uv(u+v), 0 <u<v< 1.

4.4.24 14.

4.4.25(a)^1516 ;(b) 1024675 ;(c)(0.8)^4.

4.4.26 0. 824.

4.4.27 8.

4.4.28(a) 1. 13 σ;(b)0. 92 σ.

4.4.30(40,124),88%.

4.4.32(180,190) and (195,210).

4.5.3 1 −

( 3

4

)θ

+θ

( 3

4

)θ

log

( 3

4

)

,θ=1, 2.

4.5.4 0 .17; 0. 78.

4.5.8n=19or20.

4.5.9γ

( 1

2

)

=0.062;γ

( 1

12

)

=0. 920.

4.5.10n≈73;c≈ 42.

4.5.12(a) 0.051; (b) 0.256; 0.547; 0. 780.

4.5.13(a) 0.154; (b) 0. 154.

4.5.14(1) 0.11514; (2) 0.0633.

4.6.5(b)t=− 3 .0442,p-value = 0.0033.

4.6.6(b)t=2.034,p-value = 0.06065.

4.7.1p-value = 0.0184.

4.7.2 8. 37 > 7 .81; reject.

4.7.4b≤8orb≥ 32.

4.7.5 2. 44 < 11 .3 ; do not reject H 0.

4.7.6 6. 40 < 9 .49 ; do not reject H 0.

4.7.7χ^2 =49.731,p-value = 1. 573 e−09.

4.7.8k=3.

4.8.5F−^1 (u) = log[u/(1−u)].

4.8.7For 0<u<(1/2) :

F−^1 (u) = log[2u].

For (1/2)<u<1:

F−^1 (u) = log[2(1−u)].

4.8.8F−^1 (u) = log[−log(1−u)].

4.8.18(a)F−^1 (u)=u^1 /β;

(b) e.g., dominated by a

uniform pdf.

4.9.4(a)βlog 2.

4.9.8Usesx=20.41;sy=18. 59.

4.9.10(a)y−x=9.67;

20 possible permutations;

(c)Pnn/nn.