Variance of a standard uniform variable

Question

A random variable $X$ is uniformly distributed on the interval $(0,1)$ . What is its variance?

Short answer

$1/12$ . The mean is $\tfrac12$ and $E[X^2]=\int_0^1x^2\,dx=\tfrac13$ , so $\operatorname{Var}(X)=\tfrac13-\tfrac14=\tfrac1{12}$ .

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Lessons behind this question

Continuous Random Variables and Probability Density Functions
Covariance and Correlation
Cumulative Distribution Functions

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