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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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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