Means and Variances of Random
Variables
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