Suppose that the probability distribution of a random variable x can be described by the formula P(x) = x 15 For each of the values x = 1, 2, 3, 4, and 5. For example, then, P(x = 2) = p(2) = 2/15, A: Write out the probability distribution of x. B: Show that the probability distribution of x satisfies the properties of a discrete probability distribution. C: Calculate the mean of x. D: Calculate the variance, o~2 and the standard deviation, o~ x` x`