The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value.

Overview

The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value. For a discrete random variable, $X$, the expected value is

$$ E(X) = \sum_{x} x P(X=x) $$

for a continuous variable with probability density function $p(x)$,

$$ E(X) = \int_{-\infty}^{\infty} x p(x) dx $$

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