2. Rejection Sampling Consider the function 9(3) = 0032023) x |:r:3 + z - 2| x 1,e(_,,_.25,u(o.n. In this problem, we use rejection sampling to generate random variables with pdf f(a:) = cg(:r) . (:1) Plot 9 over its domain. What is a uniform proposal distribution q that covers the support of f? What is a constant M such that the scaled target distribution p(z) = M 9(3) satises 33(3) 5 9(3) for all :r? (b) Suppose you run rejection sampling with target p and proposal 9 from part (a) until you generate 11 samples and your sampler runs a total of N 2 n times, including 11 acceptances and N - n rejections. Explain how you can use n,N and M to estimate c. (c) Use rejection sampling to generate a sample of size 103 from f and overlay a line plot of f atop a. normalized histogram of your samples. Repeat this step with 106 samples. Hint: to plot I. rst use your values of n. N and M to estimate c using your answer from part (b)