Let X be a random variable that is uniformly distributed over the interval (0, 100). Form a new random variable Y by rounding X to the nearest integer. In MATLAB code, this could be represented by Y = round(X). Finally, form the random round-off error according to Z = X - Y. Using analytical methods, find the PDF of Z as well as the mean-squared value, E[Z^2] Using MATLAB, create a histogram for the probability densities for the random variable Z. Compare with the PDF found analytically in part (a). Let X be a random variable that is uniformly distributed over the interval (0, 100). Form a new random variable Y by rounding X to the nearest integer. In MATLAB code, this could be represented by Y = round(X). Finally, form the random round-off error according to Z = X - Y. Using analytical methods, find the PDF of Z as well as the mean-squared value, E[Z^2] Using MATLAB, create a histogram for the probability densities for the random variable Z. Compare with the PDF found analytically in part (a)