The variance of a binomial random variable X with n trials and p probability of success, where p is greater than 0,
A)will always be less than the expected value of X.
B)will always be equal to the expected value of X.
C)will always be greater than the expected value of X.
D)may be less than, equal to, or greater than the expected value of X.
E)has no relationship to the expected value of X.

Question

Quizplus · Accepted Answer

The variance of a binomial random variable X is given by np(1-p), and the expected value is np. Since p is a probability, it lies between 0 and 1, making 1-p also a positive fraction less than 1. Multiplying np by a fraction less than 1 results in a value less than np, meaning the variance will always be less than the expected value.

The Variance of a Binomial Random Variable X with N