(1) Suppose that the time to repair a machine is exponentially distributed with
ID: 3056653 • Letter: #
Question
(1) Suppose that the time to repair a machine is exponentially distributed with mean 2.
(a) What is the probability that a repair takes more than two hours?
(b) What is the probability that the repair takes more than ve hours given that it takes more than three hours?
(2) Trac on Clinton Highway follows a Poisson process with rate 6 cars per minute. A deer runs out of the woods and tries to cross the road. Suppose the deer is hit by a car if a car is passing while the deer is on the road.
(a) Find the probability that the deer is hit by a car if it takes the deer 5 seconds to cross the road.
(b) What is the probability that the deer is hit by a car if it takes the deer 2 seconds to cross the road?
Explanation / Answer
1)
a) Mean = 2
Let T be the time of completion of repair. we are given P(T t) = 1 e^(t/2) . So P(T t) = e^(t/2) . (Here t is taken to be in hrs.) So,
probability repair takes more than 2hrs equals e (2/2) = e^(1) = 0.368
b) probability repair takes more than 5hrs given that it takes more than 3hrs, is P(T > 5, T > 3)/P(T > 3)
P = e ^(5/2)/e^(3/2) = e^(1) = 0.368
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