Suppose X1, X2, . . . are IID Poi(u) random variables and Xn = 'Sxi (*) i= 1 What is the approximate normal distribution of 1/(1 + X,) when n is large? Assume, Xi~Poisson () = M) 7 E ( x 1 ) = M , Vaz ( X 1 ) = / " By Central limit themem, Xn ~ N ( E (X1) , Van ( X1) ) By . Delta Method , 8 ( In ) & N ( 9 ( 1) , (8 ( 4) ) in ) : 9 ( 2 ) = - 1+ 2 -7 9 (2 ) = - ( 1 + x ) 2 # 9 ( 2 ) ) 2 2 - (1 + x ) 4 : 9 ( x n ) = 1 7 9 ( 4 ) =1 1 + M a N ItxnFollow the explanation above to answer the following question 4 1. Suppose X1, X2, ... are IID Geo(p) random variables and n Xn = Xi n i=1 What is the approximate normal distribution of H 1 + Xn when n is large