724 Answers to Selected Exercises2.5.9^12.2.4.4 815.2.4.5^78.
2.4.62; 2.2.4.82(1−y(^3) )
3(1−y^2 ),^0 <y<^1.
2.4.9^12.
2.4.12^49.
2.4.134; 4.
2.6.1(g)2+33+6yy+3+6zz.
2.6.2(a)^16 ;0;
(b) (1−t 1 )−^1 (1−t 2 )−^1 (1−t 3 )−^1 ;yes.
2.6.3pdf is 12(1−y)^11 , 0 <y< 1.
2.6.4pmf isy
(^3) −(y−1) 3
63.
2.6.6σ 1 (ρ 12 −ρ 13 ρ 23 )/σ 2 (1−ρ^223 );
σ 1 (ρ 13 −ρ 12 ρ 23 )/σ 3 (1−ρ^223 ).
2.6.9(a)^34.
2.7.1joint pdfy 2 y 32 e−y^3 , 0 <y 1 < 1 ,
0 <y 2 < 1 , 0 <y 3 <∞.
2.7.2 2 √^1 y, 0 <y< 1.
2.7.3 4 √^1 y, 0 <y<1; 8 √^1 y, 1 ≤y< 9.
2.7.7 24 y 2 y 32 y^34 , 0 <yi< 1.
2.7.8(a) 169 ; 166 ; 161 ;(b)
( 3
4 +
1
4 e
t)^6.
2.8.2^83 ;^29.
2.8.3 7.
2.8.5 2 .5; 0. 25.
2.8.7−5; 30. 6.
2.8.8√σ^1
σ^21 +σ^22
.
2.8.10 0. 265.
2.8.12 22 .5; 65. 25.
2.8.13√ μ^2 σ^1
σ^21 σ^22 +μ^21 σ^22 +μ^22 σ^21
.
2.8.15 0. 801.
Chapter 3
3.1.1^4081.3.1.41-pbinom(34,40,7/8)=0.6162.3.1.5P(X≥20) = 0.0009.
3.1.6 5.
3.1.11 163.3.1.13^6581.3.1.15( 1
3)( 2
3)x− 3
,x=3, 4 , 5 ,....3.1.16 725.3.1.18(a) Negative binomial, parame-
tersrandT/N.3.1.19(b) Code:ps=c(.3,.2,.2,.2,.1)
coll=c()
for(i in 1:10000)
{coll<-c(coll,multitrial(ps))}
table(coll)/10000
3.1.20(a) -$2.403.1.22^16.3.1.23 62524.3.1.25(a)^116 ;(b)x 21 ;(c)^116.3.1.26^254.3.1.30(a) 0.0853; (b) 0.2637; (c) 0.0861,
0.2639.
3.2.1 0. 09.
3.2.4 4 xe−^4 /x!,x=0, 1 , 2 ....3.2.5 0. 84 .,0.9858.
3.2.11About 6. 7.
3.2.13 8.
3.2.14 2.
3.2.16(a)e−^2 exp{(1 +et^1 )et^2 }.