Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.20.2 , 0.30.3 , and 0.50.5 , respectively. what is the standard deviation of this customer's book purchases?

E [x] = Expected value of X

μ = average

σ = standard deviation

V (X) = Variance

σ = (V (X)) ^ 0.5

E [X] = X * P (x)

Assuming that the number of books purchased is a discrete random variable with mean μ = E [X]

Then the variance of X can be written as V (X) = E [X-μ]^2

We started finding the average μ

μ = 0 * 0.20 + 1 * 0.30 + 2 * 0.50

μ = 1.3

Once the average is found, we can calculate the value of the variance

V (X) = 0.20 * (0-1.3) ^ 2 + 0.30 * (1-1.3) ^ 2 + 0.50 * (2-1.3) ^ 2

V (X) = 0.61

Now we know that from the variance the standard deviation can be obtained by doing:

σ = (V (X)) ^ 0.5

Finally

σ = 0.781