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 barber-shop 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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