Question: Let X be distributed Bernoulli P[X 1] p and P[X 0] 1p. (a) Show that p E[X]. (b) Write down

Let X be distributed Bernoulli P[X Æ 1] Æ p and P[X Æ 0] Æ 1¡p.

(a) Show that p Æ E[X].

(b) Write down the moment estimator b p of p.

(c) Find var

£

b p

¤

.

(d) Find the asymptotic distribution of p

n

¡

b p ¡p

¢

as n!1.

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