3.1-8. A random variable X represents the value of coins (in cents) given in change when purchases are made at a particular store. Suppose the probabilities of 1.54, 104, 254, and 50% being present in change are 0.35, 0.25, 0.20, 0.15, and 0.05, respectively.

a) Write an expression for the probability density function of X. b) Find the mean of X.