Suppose X1, Xz, . .. are IID Poi(#) random variables and Xn = -Ex. (* ) What is the approximate normal distribution of 1/(1 + X.) when n is large? Assume, XinPoisson ( ) = /) 7 E ( X1 ) = / , Vaz ( *1 ) =/ By Central limit themem, Xu & N( E (X1) , Van (*) ) 7 Xn E N ( M , MM ) Ed By. Delta Method, 8 ( Zn) & N ( 9(N), 18 ( 4) ) ) .: 9 ( 2 ) = 1 (Itx)2 + (8'( 2) ) = ( 1 + 2 ) 4 : 9 ( xn ) = 7 9 ( 4 ) = _4 1. Suppose X1, X2, ... are IID Geo(p) random variables and Xn = - Xi n What is the approximate normal distribution of 1 + Xn when n is large