Let
, be a sequence of IID random variables uniformly distributed over Suppose we form the sum
![](https://test.transtutors.com/qimg/3cdae7eb-5ca5-4aab-a300-c97067d9666f.png)
First, find the mean and variance of . Then write a MATLAB program to estimate the PDF of .
Compare the estimated PDF with a Gaussian PDF of the same mean and variance.
Over what range of Z is the Gaussian approximation of the PDF within 1% of the true PDF? Repeat this problem for ![](https://test.transtutors.com/qimg/a01e8bae-6674-4e1c-8d7c-874caccd813b.png)