c) Let Ô₁ = X₁+2X₂+2X3-X4 one of the two estimators is more efficient? and Ô₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which

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 4CR
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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
c)
Let Ô₁
=
X₁+2X₂+2X3-X4
4
f(x; 0) =
0xe
xc!
for x = 0,1,2,...
elsewhere
¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Which
one of the two estimators is more efficient?
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 c) Let Ô₁ = X₁+2X₂+2X3-X4 4 f(x; 0) = 0xe xc! for x = 0,1,2,... elsewhere ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Which one of the two estimators is more efficient?
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