Let x1,X2,.... ,Xn be a random number from a sample from the density a) f(x,0) = 0(1+æ)-(1+0), x > 0 Find the MLE of 0 and use Cramer-Rao lower bound to find large sample variance of the estimator. Suppose a random sample of size n is taken from a population X that has pdf f(x, 0) = 0" (1 – 0) x = 0,1,2,...... Illustrate that MVB unbiased estimators are necessarily MLES by obtaining MVBUE estimator of 1-0

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Let x1,X2,.... ,Xn be a random
number from a sample from the density
a)
f(x, 0) = 0(1+æ)-(1+0),
x > 0
Find the MLE of 0 and use Cramer-Rao lower
bound to find large sample variance of the
estimator.
Suppose a random sample of size n is taken
from a population X that has pdf
f(x, 0) = 0" (1– 0) x = 0,1,2,......
Illustrate that MVB unbiased estimators are
necessarily MLES by obtaining MVBUE
estimator of
1-0
Transcribed Image Text:Let x1,X2,.... ,Xn be a random number from a sample from the density a) f(x, 0) = 0(1+æ)-(1+0), x > 0 Find the MLE of 0 and use Cramer-Rao lower bound to find large sample variance of the estimator. Suppose a random sample of size n is taken from a population X that has pdf f(x, 0) = 0" (1– 0) x = 0,1,2,...... Illustrate that MVB unbiased estimators are necessarily MLES by obtaining MVBUE estimator of 1-0
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