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Then the variance of the MLE can be computed as Varˆα MLE = Var 2(n 1 n 2)−n n = 4 n2 Varn 1 n 2 4 n2 (Varn 1Varn 22Cov(n 1,n 2)) We note that n 1 and n 2 are both Binomial random variables with n trials and success probability 1α 4, so Varn 1 = Varn 2 = n 1α 4 3−α 4 Now we defineP YRutka, R Smarzewski / J Math Anal Appl 3 (12) 78â€"85 Ï Î± = 1 (α!c α ) 2 = 1 α!ö v ¸ n " , ó s î u
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