(a) [5 marks] Show that the probability of accepting a proposed X in step 2 or 3 is˜f (X)K ˜g(X)In other words, calculate the probability that the proposed value is accepted in asingle iteration of the algorithm.(b) [2 marks] Show that the probability that step (3) must be carried out is1 −R l(x)dxKZg(c) [7 marks] Implement the above algorithm in R for ˜f (x) = exp−(x−4)22and˜g(x) = exp(−|x − 4|) by choosing an appropriate l(x) and K. Plot a histogram ofyour generated samples and overlay the target density f as a line. Provide the codeyou have used to generate the histogram in your report.(d) [2 marks] Explain why this algorithm would be beneficial compared to a standardrejection sampling algorithm using the result in (b).