Question: Problem 2. (30 points) (a) Cars cross a certain section of a one-way road according to a Poisson process with rate cars per minute. If

Problem 2. (30 points) (a) Cars cross a certain section of a one-way road according to

a Poisson process with rate cars per minute. If a deer blindly runs across the road and it

takes the deer t minutes to cross the road, then what is the probability that it will be hit?

(Assume that if the deer is on the road when a car passes by, then it will be hit.)

(b) Suppose in part (a) that the deer is agile enough to escape from a single car, but if it

encounters two or more cars while attempting to cross the road, then it will be hit. What is

the probability that the deer will be hit if it takes it t minutes to cross the road?

(c) Suppose in part (a) that it takes the deer an exponentially distributed amount of time

to cross the road with a mean of t minutes. What is the probability that it will be hit?

(d) Suppose that the road is now open to two-way trac. The eastbound trac still follows

a Poisson process with rate cars per minute and the westbound trac follows a Poisson

process with rate cars per minute. What is the percentage increase in the probability that

the deer discussed in part (a) would be hit after this change in the trac conditions?

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