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Suppose that independent observations z1,, Bernoulli distribution with pmf f(z\p) = p* (1 – p)'- on z= 0,1, with 0

Suppose that independent observations z1,, Bernoulli distribution with pmf f(z\p) = p* (1 – p)'- on z= 0,1, with 0

MATLAB: An Introduction with Applications
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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Suppose that independent observations 21, 72, ...,In are available from the Bernoulli distribution with pmf f(z\p) = p* (1 – p)*- on r= 0,1, with 0<p< 1. Write 7 = E1 74/n for the sample mean. (a) Show that log f(æ\p): dp P(1 – p)* (b) The Cramér-Rao lower bound for the variance of any unbiased estimator of p can be written in the form 1 CRLB nE log f(X \p) dp Use this formula to evaluate the CRLB. Hint: Remember that V(X)= E(X – p)². (c) Show that p- X is the minimum variance unbiased estimator (MVUE) of p.
Transcribed Image Text:Suppose that independent observations 21, 72, ...,In are available from the Bernoulli distribution with pmf f(z\p) = p* (1 – p)*- on r= 0,1, with 0<p< 1. Write 7 = E1 74/n for the sample mean. (a) Show that log f(æ\p): dp P(1 – p)* (b) The Cramér-Rao lower bound for the variance of any unbiased estimator of p can be written in the form 1 CRLB nE log f(X \p) dp Use this formula to evaluate the CRLB. Hint: Remember that V(X)= E(X – p)². (c) Show that p- X is the minimum variance unbiased estimator (MVUE) of p.
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