Expected value (E(X))

How to read it

OpenStax’s Introductory Statistics calls the expected value the long-term average: the average you would expect after doing an experiment over and over. To find it, multiply each value by its probability and add the products. Its example is a soccer team that plays 0, 1 or 2 days a week with probabilities 0.2, 0.5 and 0.3, so the expected value is 0 × 0.2 + 1 × 0.5 + 2 × 0.3 = 1.1 days a week. Grinstead and Snell’s Introduction to Probability (Dartmouth) define E(X) the same way and add that it is often called the mean and written μ for short. OpenStax’s Contemporary Mathematics writes the same sum with the outcomes’ values and probabilities, Σ n(O) × P(O).

Also searched as: E of X, E(X), E[X], expectation, expected value symbol, mean of a random variable.

E(X) and μ

They are the same number. Grinstead and Snell write E(X) and μ interchangeably; OpenStax’s Introductory Statistics uses μ, the population mu, for the expected value of a discrete probability distribution. It is different from the sample mean x̄, the average of the data actually collected.