1. ## Distribution

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

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 $3a^2$ with the Uniform distribution X ~ U(-a,a). Thanks and any help would be appreciated.

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

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 $3a^2$ with the Uniform distribution X ~ U(-a,a). Thanks and any help would be appreciated.
How about $P(X=-a) = P(X=a) = 1/2$ ?

3. Thank you for the help I guess this question was easier than I thought hehe