2.1-7 Let a random experiment be the cast of a pair of unbiased dice, each having six faces, and let the random variable X denote the sum of the dice. (a) With reasonable assumptions, determine the p.m.f. (probability mass function) of X. HINT: Picture the outcome space consisting of the 36 points (result on the first die, result on the second die), and assume that each has a probability of 1/36. Find the probability for each possible value of X, namely, x = 2, 3, 4, ..., 12. (b) Draw the probability histogram for f(x). (c) Compute the mean μ and the variance σ^2 of the distribution.