i) Let X be a random variable with the PDF f(x: 0) =e-(1-", 00, S(x; A, jµ) = { ^†" -e/", x<0, where A>0 and u> 0 are unknown parameters. Find (simple) sufficient statistics for (A, u) and determine the MLES (A, î) of (A. µ). Now suppose that n 1. Is A an unbiased estimator of A? Justify your answer.

MATLAB: An Introduction with Applications
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i) Let X be a random variable with the PDF
f(x: 0) =e-(--, 0<x<o,
where 0 has a prior distribution the exponential distribution with mean 1. Determine the
posterior distribution of 0.
Find the optimal Bayes estimator of 0 based on X under quadratic loss.
(ii) Let X, ..., X, be a sample from the PDF
-e-/A, x>0,
(x; A, µ) = { ^†"
-e/". x<0,
where A> 0 and u > 0 are unknown parameters. Find (simple) sufficient statistics for
(A, u) and determine the MLES (A, î) of (A, µ).
Now suppose that n 1. Is A an unbiased estimator of A? Justify your answer.
Transcribed Image Text:i) Let X be a random variable with the PDF f(x: 0) =e-(--, 0<x<o, where 0 has a prior distribution the exponential distribution with mean 1. Determine the posterior distribution of 0. Find the optimal Bayes estimator of 0 based on X under quadratic loss. (ii) Let X, ..., X, be a sample from the PDF -e-/A, x>0, (x; A, µ) = { ^†" -e/". x<0, where A> 0 and u > 0 are unknown parameters. Find (simple) sufficient statistics for (A, u) and determine the MLES (A, î) of (A, µ). Now suppose that n 1. Is A an unbiased estimator of A? Justify your answer.
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