Variance on the unit interval

Topic: Random variables and distributions · more questions on this topic
‹ Expected number of red balls An affine image of a uniform variable ›

Let X be uniform on [0,1]. Calculate \operatorname{Var}(X).

Worked answer (click to show)

By symmetry \mathbb{E} X=1/2. And \mathbb{E} X^2=\int_0^1 x^2\,\,\mathrm{d} x=1/3, so \operatorname{Var}(X)=1/3-1/4=1/12.