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 examples, 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 and standard deviation.

In each case, sketch the two specified normal curves on the same set of axes: A normal curve with = 20 and o = 3, a normal curve with = 20 and o = 6.