Let Y1, Y2.... Y, denote a random sample from the density function given by y > 0, fy[a, 0) = elsewhere, where a > 0 is known. a Find the MLE ô of 0. b Find the expected value and variance of ê. c. Is the MLE êô an unbiased estimator for 0?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 27T
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2.Handin
Let Y1, Y2, .,Yn denote a random sample from a power family distribution with parameter 0.
(@y®-1
ful®) = -
30
0<y< 3,
0,
elsewhere.
2.1. Show that E (Y) =
30
- and derive the method of moments estimator for 0.
0+1
2.2. Show that this MoM estimator is unbiased.
Transcribed Image Text:2.Handin Let Y1, Y2, .,Yn denote a random sample from a power family distribution with parameter 0. (@y®-1 ful®) = - 30 0<y< 3, 0, elsewhere. 2.1. Show that E (Y) = 30 - and derive the method of moments estimator for 0. 0+1 2.2. Show that this MoM estimator is unbiased.
6. Handin
Let Y1, Y2, ..., Y, denote a random sample from the density function given by
(r(@)0«
y > 0,
f(y[a, 0) =
| 0,
elsewhere,
where a > 0 is known.
a Find the MLE Ô of 0.
b Find the expected value and variance of ê.
c. Is the MLE ô an unbiased estimator for 0?
Transcribed Image Text:6. Handin Let Y1, Y2, ..., Y, denote a random sample from the density function given by (r(@)0« y > 0, f(y[a, 0) = | 0, elsewhere, where a > 0 is known. a Find the MLE Ô of 0. b Find the expected value and variance of ê. c. Is the MLE ô an unbiased estimator for 0?
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