# Distribution

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• Nov 20th 2008, 02:46 PM
slevvio
Distribution
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.
• Nov 20th 2008, 04:59 PM
awkward
Quote:

Originally Posted by 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.

How about \$\displaystyle P(X=-a) = P(X=a) = 1/2\$ ?
• Nov 21st 2008, 12:40 AM
slevvio
Thank you for the help I guess this question was easier than I thought hehe