Can someone please help with this?

5.68 If we use the Metropolis Algorithm rather than the Accept/Reject Algorithm we are freed from verifying the supremum condition of the Accept/Reject Algorithm. Of Section 6.8 MISCELLANEA 267 course, we give up the property of getting random variables with exactly the dis- tribution we want and must settle for an approximation. (a) Show how to use the Metropolis Algorithm to generate a random variable with an approximate Student's t distribution with v degrees of freedom, starting fronm n(0, 1) random variables (b) Show how to use the Accept/Reject Algorithm to generate a random variable with a Student's t distribution with v degrees of freedom, starting from Cauchy random (c) Show how to use transformations to generate directly a random variable with a (d) For v 2,10, 25 compare the methods by generating a sample of size 100. Which (Mengersen and Tweedie 1996 show that the convergence of the Metropolis Algorithm variables Student's t distribution with v degrees of freedom method do you prefer? Why? is much faster if the supremum condition is satisfied, that is, if sup f/g S M