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Mathematics · Glossary

What is Expectation, variance, standard deviation?

Also known as: expectation · variance

Definition 33.2 High School Mathematics · Chapter 33 — Random Variables and the Binomial Distribution

The expectation of XX is

E(X)=∑i=1kpi xi,\E(X) = \sum_{i=1}^{k} p_i\, x_i ,

its variance and standard deviation are

V(X)=E((X−E(X))2)=∑i=1kpi(xi−E(X))2,σ(X)=V(X).\V(X) = \E\bigl((X - \E(X))^2\bigr) = \sum_{i=1}^k p_i\bigl(x_i - \E(X)\bigr)^2, \qquad \sigma(X) = \sqrt{\V(X)} .
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