Given the following probabilities for the random variable X : x 20 40 60 so 100 fx(:c) 0.1 0.2 0.4 0.2 1: (a) Fill in the ? (b) Calculate the mean (i.e., expected value) p: and variance 0'2 of X. (c) Calculate the probability distribution for the random variable Y = (X p)/cr. (d) Show that the mean of Y is O and the variance of Y is 1