# Statistics

posted by
**Kelly**
.

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.

The answer is 3.667 for part (c). Our formula begins 1(1/15) + 2(2/15) +

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 µ = 20 and o = 3, a normal curve with µ = 20 and o = 6.