Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Question

Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Edition 3ISBN: 978-9352863501

Introduction to Econometrics 3rd Edition by James Stock, Mark Watson

Edition 3ISBN: 978-9352863501

Exercise 25

Let Ybe a Bernoulli random variable with success probability Pr(Y = 1) = p, and,let Y 1 , …, Y n be i.i.d. draws from this distribution. Let
$Let Ybe a Bernoulli random variable with success probability Pr(Y = 1) = p, and,let Y 1 , …, Y n be i.i.d. draws from this distribution. Let be the fraction of successes (Is) in this sample. a. Show that = Y. b. Show that is an unbiased estimator of p. c. Show that var( ) =p(l - p)/n.$ be the fraction of successes (Is) in this sample.
a. Show that
$Let Ybe a Bernoulli random variable with success probability Pr(Y = 1) = p, and,let Y 1 , …, Y n be i.i.d. draws from this distribution. Let be the fraction of successes (Is) in this sample. a. Show that = Y. b. Show that is an unbiased estimator of p. c. Show that var( ) =p(l - p)/n.$ = Y.
b. Show that
$Let Ybe a Bernoulli random variable with success probability Pr(Y = 1) = p, and,let Y 1 , …, Y n be i.i.d. draws from this distribution. Let be the fraction of successes (Is) in this sample. a. Show that = Y. b. Show that is an unbiased estimator of p. c. Show that var( ) =p(l - p)/n.$ is an unbiased estimator of p.
c. Show that var(
$Let Ybe a Bernoulli random variable with success probability Pr(Y = 1) = p, and,let Y 1 , …, Y n be i.i.d. draws from this distribution. Let be the fraction of successes (Is) in this sample. a. Show that = Y. b. Show that is an unbiased estimator of p. c. Show that var( ) =p(l - p)/n.$ ) =p(l - p)/n.

Explanation

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We are told that:
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is a Bernoulli ra...