Question: I need help with the following problem Problem 5. Metropolis-Hastings (10 pts) We want to simulate from a discrete Cauchy distribution using a Metropolis-Hastings algorithm.

I need help with the following problem

Problem 5. Metropolis-Hastings (10 pts) We want to simulate from a discrete Cauchy distribution using a Metropolis-Hastings algorithm. The discrete Cauchy distribution has probability distribution given by 6 P(X = n) = 7272: (n>1). The proposal distribution is given as follows for a current state i: . We move to i + 1 with probability 1/4; We move to i-1 with probability 1/4; . We move to state 1 with probability 1/2. (a) Determine all transitions that would be accepted with probability 1. (b) Assume that Xn = 4, what is the probability that Xn+1 = 4? Problem 5. Metropolis-Hastings (10 pts) We want to simulate from a discrete Cauchy distribution using a Metropolis-Hastings algorithm. The discrete Cauchy distribution has probability distribution given by 6 P(X = n) = 7272: (n>1). The proposal distribution is given as follows for a current state i: . We move to i + 1 with probability 1/4; We move to i-1 with probability 1/4; . We move to state 1 with probability 1/2. (a) Determine all transitions that would be accepted with probability 1. (b) Assume that Xn = 4, what is the probability that Xn+1 = 4

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