Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 < 1). Let X₁, X₂, X, 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=1 Xj. (c) Find the maximum likelihood estimator (mle) of 0.
Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 < 1). Let X₁, X₂, X, 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=1 Xj. (c) Find the maximum likelihood estimator (mle) of 0.
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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Transcribed Image Text:Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 <
0 < 1). Let X₁, X₂, X, 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=1 Xj.
(c) Find the maximum likelihood estimator (mle) of 0.
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