Distribution

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November 20th 2008, 02:46 PM
slevvio

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.
November 20th 2008, 04:59 PM
awkward

Quote:

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 $P(X=-a) = P(X=a) = 1/2$ ?
November 21st 2008, 12:40 AM
slevvio

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