1. In this question, we will study the Poisson distribution, a distribution of a discrete random variable that is determined by a rate parameter A. If an random variable X follows the Poisson distribution with rate A, denoted as Pois()), then P(X = k) = K! k = 0, 1, 2, .. . . It is known that for such a distribution, E(X ) = A and Var(X) = A. Given X1, . .., Xn~ Pois()), the MLE of the rate parameter AMLE = 12, X, = X, is the same as the sample mean. Assume we observe 100 random variables X], . .. , X100 ~ Pois(4). (a) (1 pt) What are the bias and variance of the MLE of the rate parameter A using these 100 observations.? (b) (0.5 pt; ) Write down a 90% confidence interval of A using these 100 observa- tions. i.e., the confidence interval will be a function of X1, . . . , X100. (c) (1 pt) Use R to generate 100 IID random points from Pois(4), show the histogram. What is the value of MLE using these 100 points