Problem on metropolis-hastings algorithm

Question

Solve the following problem:

Calculate the mean of a t...

Student's t density with ν degrees of freedom, Tν, is given by

f(x|v) = r(v+1/2)/r(v/2) (1/√vπ) (1+ x²/v)^-(v+1)/2

Calculate the mean of a t distribution with ν = 4 degrees of freedom using a Metropolis- Hastings algorithm with candidate density

a. N (0, 1);

b. t with ν = 2 degrees of freedom.

In each case monitor the convergence across iterations.