Question

1. Let X be a continuous random variable with pdf

f(x)= (3/16 x^2 2<x<2

0 otherwise.

(a) Find the CDF of X

(b) Find the median,x0.5 ,of X

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2. Brad and Chad meet at the local CrossFit gym and hit it off. However, since then they’ve only run in to each other a couple of times. Suppose Brad arrives at the gym

(t =0),and that he always arrives before Chad. Let X be the duration of time Brad spends working out. On average, he spends 2 hours at the gym. Let Y be the amount

of time until Chad arrives at the gym. On average, he arrives 1.5 hours after Brad arrives. Finally, assume that the time Brad spends at the gym is independent of the

time of Chad’s arrival.

a. What’s the probability that Brad spends 3 or more hours at the gym today?

b. What’s the probability that Brad and Chad’s time at the gym overlaps?

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Answer 1

Solution 1: