Random Variables and Probability Distributions — Expectation (mean) and variance of a discrete random variable

About this lesson

This unit teaches students how to calculate the expectation (mean), variance, standard deviation, and coefficient of variation for a discrete random variable. It begins by explaining that expectation is the central value around which the possible values of the random variable accumulate, and variance measures the dispersion from that mean. The unit provides formulas for expectation (sum of x times its probability) and variance (sum of x squared times probability minus the square of the mean), and defines standard deviation as the square root of variance. It also introduces the coefficient of variation as a relative measure of dispersion, calculated as the standard deviation divided by the mean, expressed as a percentage, which is useful for comparing datasets with different units or means. Throughout the unit, students work through worked examples and exercises that involve finding missing probabilities from probability distribution tables, computing expectation and variance for given distributions, and applying these concepts to real-world contexts such as exam scores in history and geography, lifetimes of electric lamps, and drawing cards from a box with numbers. By the end of the unit, a student should be able to determine the expectation, variance, standard deviation, and coefficient of variation for a discrete random variable, and interpret the coefficient of variation to compare the relative dispersion of different datasets.