Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig

722 Answers to Selected Exercises

1.4.18(a) 116.

1.4.20^17.

1.4.21(a) 1−

( 5

6

) 6

,(b)1−e−^1.

1.4.23^34.

1.4.25^4364.

1.4.27(a)

∑ 20

x=1^4 /[20(25−(x−1))]

(b)x=1:20;sum(4/((25-x+1)*20))

(c) Downloadex1427.R

1.4.28 105 ·^4 · 9 ··^58 ·^4 · 7 ·^3 · 6.

1.4.29^134.

1.4.30^23.

1.4.31 0. 518 , 0 .491.

1.4.32No.

1.5.1 139 , 131 , 131 , 131 , 131.

1.5.2(a)^12 ,(b) 211.

1.5.3^15 ,^15 ,^15.

1.5.5(a)

(^13 x)( 539 −x)

(^525 ) ,x=0,^1 ,^2 ,^3 ,^4 ,5,

(b)

[( 39

5

)

+

( 13

1

)( 39

4

)]

/

( 52

5

)

.

1.5.7^34.

1.5.8For the plot downloadex158.R

(a)^14 ,(b)0,(c)^14 ,(d)0.

1.6.2(a)pX(x)= 101 ,x=1, 2 ,...,10,
(b) 104.

1.6.3(a)

( 5

6

)x− (^11)
6 x=1,^2 ,^3 ,...,
(c) 116.
1.6.4 366 ,x=0;^12 − 362 x,x=1, 2 , 3 , 4 ,5.
1.6.5(a) Downloaddex165.R.
1.6.7^13 ,y=3, 5 , 7.
1.6.8
( 1
2
)√ (^3) y
,y=1, 8 , 27 ,....
1.7.1F(x)=
√x
10 ,^0 ≤x<100;
f(x)= 20 √^1 x, 0 <x< 100.
1.7.3^58 ;^78 ;^38.
1.7.5e−^2 −e−^3.
1.7.6(a) 271 ,1; (b)^29 ,^2536.
1.7.8(a)1; (b)^23 ;(c)2.
1.7.9(b)^3
√
1 /2; (c) 0.
1.7.10^4
√
0. 2.
1.7.12(a) 1−(1−x)^3 , 0 ≤x<1;
(b) 1−x^1 , 1 ≤x<∞.
1.7.13xe−x, 0 <x<∞;modeis1.
1.7.14 127.
1.7.17^12.
1.7.19−
√
2.
1.7.20(b)fy(y)=1/(5 +y)^1.^2.
(c)dlife <-
function(y){1/(5+y)^(1.2)}.
1.7.21(a)f(x)=(5/3)e−x/1+(2/3)e−x.
(b)f=function(x)
{(1+(2/3)exp(-x))^(-5/2)}
1.7.22 271 , 0 <y< 27.
1.7.24π(1+^1 y (^2) ),−∞<y<∞.
1.7.25cdf 1−e−y, 0 ≤y<∞.
1.7.26pdf 3 √^1 y, 0 <y< 1 ,
1
6 √y,^1 <y<^4.
1.8.3 2 , 86. 4 ,− 160. 8.
1.8.4 3 , 11 , 27.
1.8.5log 100.^550 −log 50.^5.
1.8.6(a)^34 ;(b)^14 ,^12.
1.8.7 203.