Let X be a continuous random variable with probability density function 2x f(x; 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 T >X? is a maximum likelihood estimator of 0. i=1 E(X²) = 0 and Var(X²) = 0². Show that T is an unbiased, consistent and efficient estimator of 0.
Let X be a continuous random variable with probability density function 2x f(x; 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 T >X? is a maximum likelihood estimator of 0. i=1 E(X²) = 0 and Var(X²) = 0². Show that T is an unbiased, consistent and efficient estimator of 0.
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.CR: Chapter 13 Review
Problem 7CR
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Transcribed Image Text:Let X be a continuous random variable with probability density function
()-
2x
f (x; 0)
for x > 0 (and zero otherwise),
e
where 0 > 0 is an unknown parameter, and let X1, X2, ..., Xn be a random sample from
•.•
the distribution of X.
1
> X is a maximum likelihood estimator of 0.
T
-
i=1
E(X²)= 0 and Var(X²) = 0².
Show that T is an unbiased, consistent and efficient estimator of 0.
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