elsewhere. 1.1. Show that Y(n) = max(Y,, Y2, ., Yn) is sufficient for 0. 1.2. In Question 1.1, it was shown that Y(n) = max(Y,, Y2. .., Yn) is sufficient for 0. Let Y(m) be then an estimator. Is this estimator unbiased? If not, make it unbiased. Can we say that this unbiased ... estimator is MVUE? 1.3. If the unbiassed estimator in Question 1.2 is the MLE, is this MLE consistent?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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ubmission before 14:30
Question 1
Let Y1, Y2, .,Yn denote a random sample of size n from a population whose density is
given by
(3y?
fyle) = {03
0syse,
0,
elsewhere.
1.1. Show that Yn) = max(Y,, Y2, .,Yn) is sufficient for 0.
....
1.2. In Question 1.1, it was shown that Y(m) = max(Y,, Y2, ., Y,) is sufficient for 0. Let Y(n) be
then an estimator. Is this estimator unbiased? If not, make it unbiased. Can we say that this unbiased
estimator is MVUE?
1.3. If the unbiassed estimator in Question 1.2 is the MLE, is this MLE consistent?
Transcribed Image Text:ubmission before 14:30 Question 1 Let Y1, Y2, .,Yn denote a random sample of size n from a population whose density is given by (3y? fyle) = {03 0syse, 0, elsewhere. 1.1. Show that Yn) = max(Y,, Y2, .,Yn) is sufficient for 0. .... 1.2. In Question 1.1, it was shown that Y(m) = max(Y,, Y2, ., Y,) is sufficient for 0. Let Y(n) be then an estimator. Is this estimator unbiased? If not, make it unbiased. Can we say that this unbiased estimator is MVUE? 1.3. If the unbiassed estimator in Question 1.2 is the MLE, is this MLE consistent?
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