E(X) and Var(X) for continuous probability distributions

In general, you can find the expectation and variance of a continuous random variable over the entire range of $x$ using

E (X) = \int x f (x) d x

and

V a r (X) = \int x^{2} f (x) d x - (E (X))^{2}

If $X$ follows a uniform distribution then

f (x) = \frac{1}{b - a} w h e r e a \leq x \leq b

E (X) = \frac{a + b}{2}

V a r (X) = \frac{(b - a)^{2}}{12}

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