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Mathematics · Glossary

What is Expectation and variance?

Definition 35.2 High School Mathematics · Chapter 35 — Continuous Random Variables

For XX with density ff on II:

E(X)=∫It f(t)  ⁣dt,V(X)=∫I(t−E(X))2f(t)  ⁣dt=E(X2)−E(X)2.\E(X) = \int_I t\,f(t)\,\dd t, \qquad \V(X) = \int_I \bigl(t - \E(X)\bigr)^2 f(t)\,\dd t = \E(X^2) - \E(X)^2 .
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