Means and Variances of Random Variables

Recall that for a given set of numbers x1, x2, Recall that for a given set of numbers x1, x2, . . . , xn, its mean ¯x and variance s2 are defined as

A random variable X is usually described by its probability distribution Probabilities need to be took into account in calculating the mean and variance of a random variable.

Example

Mean and the Standard Deviation Suppose that X is a discrete random variable whose probability distribution is The mean (also called the expected value) μX of X is defined by .

Find the mean, variance, and standard deviation.

Rules for Means and Standard Deviations

Example