Asked by ramj
Let X1,…,Xn be i.i.d. Poisson random variables with parameter λ>0 and denote by X¯¯¯¯n their empirical average,
X¯¯¯¯n=1n∑i=1nXi.
Find two sequences (an)n≥1 and (bn)n≥1 such that an(X¯¯¯¯n−bn) converges in distribution to a standard Gaussian random variable Z∼N(0,1) .
X¯¯¯¯n=1n∑i=1nXi.
Find two sequences (an)n≥1 and (bn)n≥1 such that an(X¯¯¯¯n−bn) converges in distribution to a standard Gaussian random variable Z∼N(0,1) .