How to Calculate $\operatorname{Var}(X)$?

probability expected-value probability-distributions covariance variance

Since $X$ is uniform in the interval $[0,1]$, $E(X^2)=\int_0^1x^2dx=\frac{1}{3}$. Variance=$\frac{1}{12}$.

Related

Inner tangent between two circles formula
equivalence in Uniform convergence and space of bounded functions. Requirement of functions $f_n$ and $f$ are bounded function.
Coupling for tail bounds
Prerequisite for Takhtajan's "Quantum Mechanics for Mathematicians"
A fractional part integral giving $\frac{F_{n-1}}{F_n}-\frac{(-1)^n}{F_n^2}\ln\left(\!\frac{F_{n+2}-F_n\gamma}{F_{n+1}-F_n\gamma}\right)$
Equivalent Definitions of a Topological Manifold: Are Open Sets in $R^n$ homeomorphic to $R^n$?
How to "rotate" points through 90 degree?
A triple integral dancing in the unit cube
Best practice for the notation of conditions in cases: 'if' vs 'for' vs ','
Tiling the plane with consecutive squares
What exactly is a tensor product?
What does an outer automorphism look like?