Question

# The time you need to find a parking spot around Washington Square Park is well

modeled as an exponential

with parameter 1. Laura decides to drive to Washington Square

Park to bring a present to a friend. However, she is very forgetful: with probability 1/4 she

forgets the present and she has to go back to get it. If this happens she starts looking for

parking at 5 pm. If she doesn't forget she starts looking for parking spots at 4 pm.

a. We model this problem using an indicator random variable F that represents whether she

forgets the present or not and a continuous random variable T, which corresponds to the

time when she finds a parking spot. T = 5 means that she finds a spot at 5 pm, T = 11:5

means she finds a spot at 11:30 pm, T = 25 means she finds a spot at 1 pm the day after

and so on. What are the conditional pdfs of T given F? Sketch them.

b. Compute and plot the marginal pdf of T.

c. If T = 4:5, what is the probability that she forgot the present?

d. If she finds parking at 6 pm, what is the probability that she forgot the present? (You can express your answer as a function of e.)

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