Problem #1: (15pts) The sample space of a random experiment is {a, b, c, d, e, f, and each outcome is equally likely. A random variable X is defined as follows: outcome a b C d e f 0 0 1.5 1.5 2 3 Determine the probability mass function of X. Use the probability mass function to determine the following probabilities: (a) P(X = 1.5) (b) P(0.5 3) (d) P(0 X <2) (e) P(X = 0 or X = 2)