Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X2, X3,..., Xn has the following probability density function (exe-e x! c d f(x; 0) = 0, , for x = 0,1,2,... elsewhere X₁+2X2+2X3-X4 and 6₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which 4 Let 6₁=X₁+2X₂ one of the two estimators is more efficient? What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter 8?

A First Course in Probability (10th Edition)
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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
exe-e
x!
0,
c) Let ₁
d
X₁+2X₂+2X3-X₁
¹+2X²+2X
4
f(x; 0) =
for x = 0,1,2,...
elsewhere
and 6₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Which
one of the two estimators is more efficient?
What is the Cramer-Rao lower bound for the variance of the unbiased 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 exe-e x! 0, c) Let ₁ d X₁+2X₂+2X3-X₁ ¹+2X²+2X 4 f(x; 0) = for x = 0,1,2,... elsewhere and 6₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Which one of the two estimators is more efficient? What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter 0?
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