Problem 3 (15 points) a. (2 points) Consider an exponential random variable X with rate > > 0 (i.e., with probability density function (PDF) fx(x) = de-> for all x 2 0 and fx(x) = 0 for all r 1/X]. Explain. b. (6 points) Do Problems 3.3 and 3.4, page 164 in the text. Compute the marginal probability mass function (PMF) and the marginal cumulative distribution func- tion (CDF) of the random variable Y. c. (7 points) Consider random variables X and Y with joint probability density func- tion (PDF): fx,y(x, y) = c if 0 1, 0 otherwise. (i) Determine the value of c. (ii) Determine the probability P{0.5