Question: Write a Python program implementing the Metropolis-Hastings algorithm to sample a random variable X with the density f(x) x x-x1 , x > 0.

Write a Python program implementing the Metropolis-Hastings algorithm to sample a random

Write a Python program implementing the Metropolis-Hastings algorithm to sample a random variable X with the density f(x) x x-\x1 , x > 0. Choose the proposal density q to be exponential random variable with mean one. Choose positive numbers to start the Markov chain. (a) Plot the density function f(x). (b) Histogram the values attained by Markov chain and compare it to the plot of f(x). (c) Estimate the value of E[X] and var(X) using values of Markov chain.

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