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**slevvio** Let X be a (discrete or continuous) random variable with range $\displaystyle R_X \subset [ -a,a] $. Find a distribution so that $\displaystyle Var(X) = a^2 $.

I tried looking through the distributions and the only ones we have learned about are the uniform and the binomial that have finite ranges, when I tried working these out I failed. The closest I got was a variance of $\displaystyle 3a^2 $ with the Uniform distribution X ~ U(-a,a). Thanks and any help would be appreciated.