Question: 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.

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, \({{\sigma }^{2}}\), and the standard deviation, \(\sigma \)