5.12 Suppose that the probability distribution of a random variable X can be described by the formula P(x)= X/15 ...

     5.12 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 of x   satisfies the properties of a discrete probability distribution.   c. Calculate the mean of x.   d. Calculate the variance σ2x, and the   standard deviation, σx.