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
