Question 1. Let X1,...,X, be an independent and identically distributed sequence of random variables from a population in {ga.s |a €R, B > 0}, where Ja,3(1) = (1 - a) -e-8(z-a). I2a. You may assume in this exercise that E,8(X1) = 208+1 23 %3D Vara(X1) = . a. Derive the moment estimator of 69 = (ao, Bo). Assume from now on that B, is known! b. Derive the maximum likelihood estimator of ag.

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Question 1. Let X1,...,X, be an independent and identically distributed sequence of
random variables from a population in {ga.s |a € R, B > 0}, where
Ja,3(1) =
(1 - a)
-e-8(z-a).
I2a.
You may assume in this exercise that
E. s(X1) =
2a8+1
23
Vara.s(X1) =
a. Derive the moment estimator of 0 = (a0, Bo).
%3D
Assume from now on that B, is known!
b. Derive the maximum likelihood estimator of ao.
Transcribed Image Text:Question 1. Let X1,...,X, be an independent and identically distributed sequence of random variables from a population in {ga.s |a € R, B > 0}, where Ja,3(1) = (1 - a) -e-8(z-a). I2a. You may assume in this exercise that E. s(X1) = 2a8+1 23 Vara.s(X1) = a. Derive the moment estimator of 0 = (a0, Bo). %3D Assume from now on that B, is known! b. Derive the maximum likelihood estimator of ao.
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