Show that for any >0 and S₁ = 1X₁, lim P(|S₁ - 0 ≥ ) = 0. ε n 71-00 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Suppose that a sequence of mutually independent and identically distributed discrete random
variables X₁, X₂, X3,..., Xn has the following probability density function
f(x; 0) =
exe-0
x!
0,
7
for x = 0,1,2,...
elsewhere
a) Show that for any & > 0 and S₁ = 1X₁, lim P(|S₁ - 0 ≥ ) = 0.
72-00
b) Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0.
Transcribed Image Text:Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3,..., Xn has the following probability density function f(x; 0) = exe-0 x! 0, 7 for x = 0,1,2,... elsewhere a) Show that for any & > 0 and S₁ = 1X₁, lim P(|S₁ - 0 ≥ ) = 0. 72-00 b) Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0.
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