Estimation of Mean and Variance Using MATLAB

Question

Develop a MATLAB script that generates (N) random variables from fx(x) using the methods discussed in class. The script should ask the user for the number of samples to generate and the value (a).

a) Assume a = 1, generate 100 samples and plot the histogram. Hint, to check the distribution generate ~1000 samples.

b) Estimate the mean and variance from the previously generated N samples.

Compare the results to the analytical results below by displaying both in you script.

c) Let g(x) = 2(1-x2 ), Calculate and display E[g(x)] using the N RVs drawn from part (a).

d) Extra Credit: Analytically derive the formula for the mean.

Summary

 This question belongs to MATLAB software and discusses about application of MATLAB in statistics to estimate mean and variance of sample data.