Q:

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?

Accepted Solution

A:
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