2. Rejection Sampling Consider the function Eli\") = \"032(121\") X I553 + 53? 2I x 1:e{1,.25}u{n,1}- In this problem, we use rejection sampling to generate random variables with pdf f {1:} = cg[:1:}. (a) {2 points) Plot 9 over its domain. What is a uniform proposal distribution q that covers the support of 3"? What is a constant M such that the scaled target distribution p[:.:} = Mg(a:} satises 31(3) 1: 49(3) for all I? (b) (4 points) Suppose you run rejection sampling 1with target p and proposal g from part (a)I until you generate as samples and your sampler I'IJIIIS a total of N 33 n times, including 11 acceptances and N n rejections. Explain how you can use n? N and M to estimate c. {c} {4 points) Use rejection sampling to generate a sample of size If!3 from f and overlay a line plot of f atop a normalized histogram of your samples- Repeat this step with 105 samples. Hint: to plot f, rst use your values of n, N and M to estimate c using your answer from part (b)