Let X be a continuous random variable with probability density function 2x f(1; 0) = () -x² /0 for x > 0 (and zero otherwise), e where 0 > 0 is an unknown parameter, and let X1, X2, ..., Xn be a random sample fror the distribution of X. Show that T= = 1 >X? is a maximum likelihood estimator of 0. n i=1
Let X be a continuous random variable with probability density function 2x f(1; 0) = () -x² /0 for x > 0 (and zero otherwise), e where 0 > 0 is an unknown parameter, and let X1, X2, ..., Xn be a random sample fror the distribution of X. Show that T= = 1 >X? is a maximum likelihood estimator of 0. n i=1
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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
Transcribed Image Text:Let X be a continuous random variable with probability density function
2x
f (x; 0) =
-x²/0
for x > 0 (and zero otherwise),
where 0 > 0 is an unknown parameter, and let X1, X2, ...,Xn be a random sample from
the distribution of X.
n
Show that T
>X? is a maximum likelihood estimator of 0.
i=1
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