Let X1, X2, ... be a sample from a population that is geometricallydistributed with p = 1.(a) Use a suitable version of the Central Limit Theorem to estimate the probability800PΙΣΧ> 2450i=1(b) The negative binomial random variable was defined as a sum of a sample of geometricrandom variables. Why might this approach be preferable to just using the negativebinomial PMF?

Given: Xi ~ Geometric with p=1/4 Therefore, E[X] = μ = 1/p = 4 & Var(X) = σ2 =1/p2 -1/p = 16…

Let X1, X2, ... be a sample from a population that is geometrically distributed with p = }. (a) Use a suitable version of the Central Limit Theorem to estimate the probability 800 PEx; > 2450 (b) The negative binomial random variable was defined as a sum of a sample of geometric random variables. Why might this approach be preferable to just using the negative binomial PMF?