Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 < 1). Let X₁, X2,, X₁ be a random sample of size n from the population of X. (a) Write down the likelihood function of the parameter. (b) Show that the log likelihood function of depends on the sample only through Σj-1Xj.

Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 < 1). Let X₁, X2,, X₁ be a random sample of size n from the population of X. (a) Write down the likelihood function of the parameter. (b) Show that the log likelihood function of depends on the sample only through Σj-1Xj.

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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Question

Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 <
0 < 1). Let X₁, X2,,X₁ be a random sample of size n from the population of X.
(a) Write down the likelihood function of the parameter.
(b) Show that the log likelihood function of depends on the sample only through
Σj-1Xj.

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Follow-up Questions

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Follow-up Question

(e) Show how the mle ofis related to its mme. Explain if it is always true.
(f) Verify if XX; is a sufficient statistic for or not.
(g) Justify if = is an unbiased estimator for 0.
X

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Follow-up Question

(c) Find the maximum likelihood estimator (mle) of 0.
(d) Find the method of moments estimator (mme) of 0.

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