3-16 The sample space of a random experiment is {a, b, c, d, e, f}, and each outcome is equally likely. A random variable is defined as follows: Outcome a b c d e f x D D 1.5 1.5 2 3 Determine the probability mass function of random variable X. Use the probability mass function to determine the following probabilities. {a} ELK = D}, {bl Pill?" -: Xe: 2.8}, {c} PIX > 4], {d} P{1 S X S 2}, and PD: = 1.5 or X = 3] {b} Determine the cumulative distribution function of a random variable {c} Determine the mean and variance of the random variable