Question: 3.2 Let Y be a Bernoulli random variable with success probability Pr(Y = 1) = p, and let Y1,c, Yn be i.i.d. draws from this

3.2 Let Y be a Bernoulli random variable with success probability Pr(Y = 1) =

p, and let Y1,c, Yn be i.i.d. draws from this distribution. Let pn be the fraction of successes (1s) in this sample.

a. Show that pn = Y.

b. Show that pn is an unbiased estimator of p.

c. Show that var(pn) = p(1 - p)>n.

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