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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