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) .
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