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b. 1/64 ¢..0137,.0137—d. L817 75. a. 449,699,148 —b. .050, 018 |
17. b. 90th percentile of Y = 1.8(90th percentile of X) +3277. a.A; —_b. Exponential with 2 = .05 |
¢. 100 pth percentile of Y = a(100 pth percentile of ¢, Exponential with parameter ni |
Pare 83. a. 8257, 8257, .0636 b. .6637—¢. 172.73 |
Te askensoy tate 87. a..9296 b..2975 98.18, |
Bly QsSES2 SEES, bisOHe 89. a. 68.03, 122.09 b..3196 _€. .7257, skewness |
23. a. A+ (B— Alp |
b. (A + B)2, (B — AP/12, (B — A)/VT2 on a tae aoe *; ae % = Aly |
BA" hyn + 1B — AN] . 148. e9.5 125: |
25. 314.79 woh |
27, 248, 3.6 95. b. P(x + B) Mm + PAP + B +m) V(BYI, Bia + B) |
29. 1/(1 = 1/4), 1/4, 16 97. Yes, since the pattern in the plot is quite linear. |
31. 1007, 307 By Yes |
33. f(a) = dy for —5 <x <5 and = 0 otherwise 101s Yes |
38. a. M@ = 180515 — 9,1 < 15: EOD = 7.167, 103. Form a new variable, the logarithms of the rainfall |
Voy) = 44.44 values, and then construct a normal plot for the new |
b. EO) = 7.167, VON) = 44.44 a Bees of the linearity of this plot, normality |
37. M() = SKS — 9, EX) = 6.667, V(X) = 44.44 ; |
This distribution is shifted left by .5, so the mean differs 105+ The sora plot lige a.cnoWliness palteni: showitg |
by 5 but the variance is the same. Dosivenkenness) |
46) iAH BoE GATT BRE 107. The plot deviates from linearity, especially at the low |
end, where the smallest three observations are too small |
€..9147 £..9599 9104 bh. 0791 AUC REE Ea se ; |
i 0668 5.9876 relative to the others. The plot works for any / because / |
is a scale parameter. |
41. a.134 b.-134 674d. 674 5 sais |
e. — 1.555 109%. fy(y) = 2", y > 1 |
43. a..9772 bd. .9104— 8413 ALO) FEW AEG |
2417 f. 6826 113. fy(9) = 16,0 <y < 16 |
48. a..7977 _ b. .0004 115. fy() = Win +9) |
¢. The top 5% are the values above .3987. 5 |
117. Y=x7/16 |
47. The second machine |
119. fr(y) = 1/2Ve,0<y <1 |
49. a..2525 b. 39.96 b= eval |
121. fr(y) = 1/l4yy, O<¥ <1, fr) = 1/[8VyI, |
51. .0510 l<y<d |
53. a..8664 = b..0124 2718 125, py(y) = (1 — p)"'p,y = 12.3.0. |
--- Trang 834 --- |
Chapter5 821 |
27a4 b.6 eFax) =4/25,0 <x < 25; 9. a. .3/380,000 b..3024—€. 3593 |
F(x) =0,.x <0; FQ) =1,x>25 12.5, 7.22 d. 10Kx7 + .05,20 << 30 eno |
129. b. F(x) = 1 — 16/(x + 4),x > 0; FQ) = 0.x <0 UL. a. p(x,y) = (e428 /x!) (e-" /y!) for x = 0, 1, 2, ..5 |
©2247 d.4 &. 16.67 y=0,1,2,... b (e*9(1+4+40)) |
ec. e*"( + 0)"/ml, Poisson with parameter 4 + 0 |
131. a..6563 b.41.55 3179 |
ae x >0,y>0 b..3996 5940 |
133. a. .00025, normal approximation; .000859, binomial a. 3298 |
b. .0888, normal approximation; .0963, binomial |
" 18. a. F(y) =1—2e +e for y > 0, FQ) =0 for |
135. a. F(x) =1.5(1 — 1), 1 Sx <3; FQ) =0,x <1; y <0; f(y) =4ie 2 — 3e* for y > 0, fy) = 0 |
FQ)=1x>3 b.9%4 ©. 1.6479 fory <0 |
d..5333 e. .2662 b. 2/62) |
137. a. 1.075, 1.075 b..0614,.3331 «2.476 i.a25 bln en |
139. b. 95,693, 1/3 d. fx(x) = 2VR7— 22 /(R?) for, -R <x <R, |
2 2 f(y) = 2,\/R? — y2/(R?) for -R < y < Ry no |
141. b. FQ) = Se, x < 0; FQ) = 1 — Sex > 0 |
€. 5, .6648, .2555, .6703 19. .15 |
143. ak=(2- 15"! db. F(X) =0,x <5; 21. L? |
=1— (Six) a = |
Fa) =1- GIN x >5 eS DIE) 95 yy |
145. b. 4602, 3636 €..5950 140.178 2528 |
2 |
147. a. Weibull by 5422 27. a, —10588 —_b. ~.0128 |
149. ai bea 1p |
@ F(t) 1—e #e *10P),0 <x < fia) =0, 3% afl) = 2x, 0 <x < 1, fs) = 0 elsewhere |
EOF =e D.fnxGlay =U O<y<x<l 6.6 |
: 2(s-"/09)) d. no, the domain is not a rectangle |
f(x) = a(1 — x/B)e Y.05x SB e. E(YIX = x) = x/2, a linear function of x |
fix) = 0,x < 0, fx) = 0.x > B £ VX =x) = x12 |
This gives total probability less than 1, so some ; |
probability is located at infinity (for items that last 39. a. f(x) = 2e°**,0 <x < 00, f(a) = 0.x < 0 |
forever). b. fxs) = "0 <x < yy < 00 |
PY > 2x = 1) = Ve |
151. jue ~ v/20, x © v/800 d. no, the domain is not rectangular |
7 e. (VIX = x) =x + 1,a linear function of x |
155. Fgh) = 818 £VYX=x)=1 |
41. a. EM X =x) = 1/2, a linear function of x; V(YI |
Chapter 5 X=y=r/2 |
b. fit, y) = 1k, 0<y <x |
1. a. .20 b. 42 . The probability of at least one ¢. fy) = —Iny),0<y <1 |
hose being in use at each pump is .70. a. EQ) = 1/4, VX) = 7/144 |
dx o 1 2 y» oOo 1 2 e. EY) = 1/4, VY) = 7/144 |
px) | 163450 pv) 24383843. a. py (OIL) = 4/17, pyx(IIL) = 10/17, pyx(2I) = 3/17 |
PX <1) =.50 b. prx(O12) = -12, prx( 112) = 28, prx(2I2) = .60 |
e. dependent, .30 = P(X = 2 and Y = 2) 4 P(X = 2) ec: 40 |
P(Y = 2) = (.50)(.38) d. pyy(012) = 1/19, pyy(112) = 3/19, pyr(212) = 15/19 |
BadS b40 © .22=P(A)=PUX,-XA>2) 4 aAMX=y=x2 bVNX=y=x°/12 |
d...17, 46 efx) =y?-10<y<l |
eon 0 1 2 3 447. a. pls!) = p22) = pB3) = 19, p21) = pBA) |
pices) 19 30 25 4 2 = p32) = 2/9 |
E(X;) = 1.7 b. px(1) = 1/9, px(2) = 3/9, px(3) = 5/9 |
¢. pyw(IIL) = 1, pyx(1I2) = 2/3, pnx(2I2) = 1/3, |
Brugge 0 1 2 3 Prx(13) = 4, prx(213) = -4, prx(3[3) = .2 |
2+ SS d. AX = 1) = 1, BX = 2) = 473, |
Pal%2) 19 30 28 23 E(VX = 3) = 18, no |
8 0 =p(4 , 0) A pi(4) - px(0) = (.12)(.19) so the two e. VOX = 1) = 0, VINX = 2) = 2/9, |
variables are not independent. VINX = 3) = 56 |
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