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(IELM313)hw1_solution.pdf
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Solution of Homework 1
1.

2.

Let X be the time to between two hits. It is follow an exponential distribution with rate 1/15. Then,



+ .x /15 .2
P(X > 30) = 1 e dx = e = 0.135.
3.

4.
Let N(t) be the total number of arrivals till time t, including both regular and VIP customers. Then N(t) is a Poisson process with rate 25/hour. Then the probability of the next customer arrives before 9:15am after 9:10am is


P(N(5)>0) = 1- P(N(5)=0) = 0.875.
5.


6. Let X denote the time it takes for a truck to go through the terminal. Let Xr denote the time it takes for a truck to go through the terminal in the regular queue, and Xs denote the time it takes a truck to go through the terminal in the screening queue. Let R1 and 2 denote two independent random numbers. Then the generators of two exponential distributions are
Xr =.10ln(1. R2 )
Xs =.25ln(1. R2 )
Then, we can develop the generator of X as
.X =.10ln(1. R ) 0 R < 0.9
r 21
.
X =. Xs =.25ln(1. R2 ) 0.9 R1 1