Let Xi, X2...-Xn be a iid. sample from Bernoulli(p) and let Yn-Σηι(X-P)/n. Show that Ya converges...

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Answer 1

Answer #1

$CDF of Yn is F, (y) = P(y, y) V p(1 P) Since from central limit theorem, (0.1) as n → oc Vnp(1 -p) where Y Σ xi ~ Binonnal(n,$

$0 if y<0 l if y >0 p(1 -p) as n→ Again at y 0 7t Hence Yn converges to degenerate distribution at 0 as n -oo.$

Answer 2

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