Class Problems on Exponential Distribution and Poisson Processes
1. The amount of time it takes to spot a defect in a cast is distributed exponentially with mean 15
minutes.
a. What is the probability of spotting a defect within 10 minutes?
b. If I have been unsuccessful in spotting a defect for the past 14 minutes, what is the expected
time from now on that I will spot it?
c. If there are four diﬀerent students working on 4 similar casts, when do you expect the ﬁrst
among the four students to spot a defect?
d. Continuing with the previous question, what is the probability that in 30 minutes exactly
two students will spot defects and two will not?
2. A barbershop has 3 servers with expected service times of 20, 15 and 10 minutes. The servers
have been busy for 5, 7 and 6 minutes respectively with their current customers. What is the
expected remaining time until the next service completion?
3. Meteorologists claim that visible meteors entering the earth’s atmosphere over our county region
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 Spring '08
 Klutke

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