Suppose X1,X2,...,Xn is a random sample from a binomial distribution. Recall X is the number of successes in m independent trials with probability of success at each trial is θ. We know that E[X] = mθ and V ar(X) = mθ(1 −θ). (a) Find the method of moment estimator for θ. (b) Is the estimator in (a) unbiased? (c) Is the estimator in (a) consistent? (d) Show that the estimator in (a) is also the maximum likelihood estimator.
Suppose X1,X2,...,Xn is a random sample from a binomial distribution. Recall X is the number of successes in m independent trials with probability of success at each trial is θ. We know that E[X] = mθ and V ar(X) = mθ(1 −θ). (a) Find the method of moment estimator for θ. (b) Is the estimator in (a) unbiased? (c) Is the estimator in (a) consistent? (d) Show that the estimator in (a) is also the maximum likelihood estimator.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. Suppose X1,X2,...,Xn is a random sample from a binomial distribution. Recall X is the number
of successes in m independent trials with probability of success at each trial is θ. We know that
E[X] = mθ and V ar(X) = mθ(1 −θ).
(a) Find the method of moment estimator for θ.
(b) Is the estimator in (a) unbiased?
(c) Is the estimator in (a) consistent?
(d) Show that the estimator in (a) is also the maximum likelihood estimator.
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