Download Homework #4

Homework #4
Problem 5
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The safety probability of 4-engine plane:
2
2
3
6p (1-p) +4p (1-p)+p4
The safety probability of 2-engine plane:
2
2p(1-p)+p
6p2(1-p)2+4p3(1-p)+p4>2p(1-p)+p2
(p-1)2(3p-2)>0, p>2/3
Problem 12
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P{0 colds/benefit}=exp(-2) (i.e., i=0); P{0
colds/not benefit}=exp(-3)
Combine the Bayes’ rule and Poisson
distribution function
P{benefit/0 colds}
=P{0/b}P{b}/(P{0/b}P{b}+P{0/nb}P{nb})
=.75e-2/(.75e-2+.25e-3)
Problem 27
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P{X>L}=0.95=P{Z>(L-2000)/85},
P{Z≦(L-2000)/85}=0.05, ∴(L2000)/85=-1.64, L=1860.6
Problem 31
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P{X>4.0×106}=1-P{X≦4.0×106}=
1-P{Z≦[(4.0×106 -4.4×106)/3.0×105]}
=0.9082>0.90, accept this contract
Problem 39
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Using the exponential C.D.F.
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The parameter λ=0.05
F(X>20)=1-F(X≦20)=1-[1-exp(0.05×20)]=exp(-1)=1/e=0.3679
If the lifetime distribution of X is uniform,
then Prob.(X>30/X>10)=(40-30)/(4010)=1/3
Problem 44
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Let W=X+Y, W~Xn2 (9)
P{W>10}=1-0.6495=0.3504 by using
the program 5.8.1a