# Statistics

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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.

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