Use the MetropolisHastings algorithm to simulate a Poisson random variable with parameter . Let T be the (infinite) matrix that describes a simple random walk

Use the Metropolis–Hastings algorithm to simulate a Poisson random variable with parameter λ. Let T be the (infinite) matrix that describes a simple random walk on the integers. From an integer i, the walks moves to i−1 or i+1 with probability 1/2 each. Show how to simulate a Poisson random variable. Then implement your algorithm and give evidence that it works.