be a Bernoulli random probability p, and let Y1,..., Y, be i.i.d. draws from this distribution. Let p be the fraction of successes (1s) in this sample. a. Show that p = Y. b. Show that p is an unbiased estimator of p. c. Show that var(ô) = p(1 – p)/n.

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Chapter1: Combinatorial Analysis
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Let Y be a Bernoulli random variable with success probability Pr(Y = 1) =
p, and let Y1, ... , Y, be i.i.d. draws from this distribution. Let p be the
fraction of successes (1s) in this sample.
a. Show that p = Y.
b. Show that p is an unbiased estimator of p.
c. Show that var(p) = p(1 – p)/n.
Transcribed Image Text:Let Y be a Bernoulli random variable with success probability Pr(Y = 1) = p, and let Y1, ... , Y, be i.i.d. draws from this distribution. Let p be the fraction of successes (1s) in this sample. a. Show that p = Y. b. Show that p is an unbiased estimator of p. c. Show that var(p) = p(1 – p)/n.
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