Part II - Metropolis Hastings SUPPDSE we have observed data. 91:921- . . ,ym sampled independently and identically distributed from the mixture distribution 5. 6. 7. 8. \"(7.052) + (1 6)N(10, 0.52). [5 points) Simulate 200' realizations from the mixture distribution above with ti = 0.7. (2 points) Draw a histogram of the data. that also includes the true density. How close is the histogram to the true density? (5 points) Now assume :5 is unknown with a Uniform[0,1} prior distribution for :5. Implement an independence Metropolis Hastings sampler with a Uniform(0,l) proposal. (5 points) Implement a random walk Metropolis Hastings sampler where the proposal 5* = 5\"} + e with r. w Uniform(l. 1). (3 points) Explain why the independence Metropolis Hastings sampler from (T) is better than the random walk Metropolis Hastings sampler from [3]