Consider the Gamma-Poisson mixing model Y~ NegBinom(r. p), With r>0 rEN pe [0, 1], if we can express Y as a marginal random variable of the ensemble model YA ~ Poisson (X), A~ Gamma(r, 3), were A> 0And 3 = is the rate parameter, namely. E[X]=r/3. We consider r = 5, p = 0.6 N = 10,000. 1. Use random number simulation in r code Y... YN NegBinom(r. p) to estimate the probability mass mass function of a Negative Binomial. That is, to construct a Monte Carlo estimator of P(Y= k) = Were k is 8 and {Y= k)| denotes the number of Y, equal to k. 2. Construct a 95% confidence interval using the estimator based on one replica using |{Y-k}| N V(S) = $(S) = - ( 12 10.) - (+216) . f(x 3. Construct a 95% confidence interval using the estimator based on 100 replicas using the empirical estimator of V (NC (S)). 4. How do the standard errors calculates by the above methods compare?