1. Write a matlab program, using polar method, to generate samples from a student's distributionwith degrees of freedom 5. Generate 1000 samples and plot a histogram.
2. In this problem, you have to derive an acceptance/rejection procedure for generating astandard normal random variable. Assume that you have a program to generate a double exponential random variable (from the previous assignment) with parameter 1 and density,
g(x) = 12exp(-|x|) .
First, find a constant c such that f(x)/g(x) ≤ c, for all x. Then, write an acceptancerejectionprogram using this values of c. Generate 1000 samples of a standard normalusing this method. What fraction of the iterations resulted in acceptance? Compare it with 1/c.