A Bernoulli randomvariable X is P X 0 1p P X 1 p (a) Propose amoment estimator b p for p (b) Find the variance of the asymptotic distribution of p n b p p (c) Use the knowledge of the Bernoulli distribution to simplify the asymptotic variance (d) Propose an estimator of the asymptotic variance of b p

Question: A Bernoulli randomvariable X is P[X 0] 1p P[X 1] p. (a) Propose amoment estimator b p for p. (b) Find

A Bernoulli randomvariable X is P[X Æ 0] Æ 1¡p P[X Æ 1] Æ p.

(a) Propose amoment estimator b p for p.

(b) Find the variance of the asymptotic distribution of p

b p ¡p

(c) Use the knowledge of the Bernoulli distribution to simplify the asymptotic variance.

(d) Propose an estimator of the asymptotic variance of b p.

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