## Question

###### Exercise_B3: Let Xi,i 1,2, be independent Bernoulli(p) random variables and let Yn = Eiz1 Xi/n. (a) Show that Vn(Yn ~ p) ~ N(0,p(1 ~ P)) in distribution: (b) Show that for p # 1/2, Vn[Yn(1~Yn)-p(1-p)] = N(0, (1~2p)?p(1-p)) in distribution Show that for p = 1/2, 4n[{ _ Yn(1 _ Yn)] ~ xZ in distribution_

Exercise_B3: Let Xi,i 1,2, be independent Bernoulli(p) random variables and let Yn = Eiz1 Xi/n. (a) Show that Vn(Yn ~ p) ~ N(0,p(1 ~ P)) in distribution: (b) Show that for p # 1/2, Vn[Yn(1~Yn)-p(1-p)] = N(0, (1~2p)?p(1-p)) in distribution Show that for p = 1/2, 4n[{ _ Yn(1 _ Yn)] ~ xZ in distribution_

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