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3. Handin Ex. 9.84 A certain type of electronic component has a lifetime Y (in hours) with probability density function given by SO10) = { () ye-®, y > 0, otherwise. That is, Y has a gamma distribution with parameters a = 2 and 0. Let ô denote the MLE of 0. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of 0. b Find Εί) and V (). c Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What is the MLE for the variance of Y?

3. Handin Ex. 9.84 A certain type of electronic component has a lifetime Y (in hours) with probability density function given by SO10) = { () ye-®, y > 0, otherwise. That is, Y has a gamma distribution with parameters a = 2 and 0. Let ô denote the MLE of 0. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of 0. b Find Εί) and V (). c Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What is the MLE for the variance of Y?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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3. Hand in 9.24 Let Y1, Y2, Y3, ...Y, be independent standard normal random variables. a What is the distribution of , Y?? b Let W, = E, Y}. Does W, converge in probability to some constant? If so, what is the value of the constant? 4. Hand in 9.30 Let Y1, Y2, ..., Y, be independent random variables, each with probability density function [ 3y², 0<y<1, f(V) = 0, elsewhere. Show that Y converges in probability to some constant and find the constant.
Transcribed Image Text:3. Hand in 9.24 Let Y1, Y2, Y3, ...Y, be independent standard normal random variables. a What is the distribution of , Y?? b Let W, = E, Y}. Does W, converge in probability to some constant? If so, what is the value of the constant? 4. Hand in 9.30 Let Y1, Y2, ..., Y, be independent random variables, each with probability density function [ 3y², 0<y<1, f(V) = 0, elsewhere. Show that Y converges in probability to some constant and find the constant.
3. Handin Ex. 9.84 A certain type of electronic component has a lifetime Y (in hours) with probability density function given by SO10) = { () ye-®, y > 0, otherwise. That is, Y has a gamma distribution with parameters a = 2 and 0. Let ô denote the MLE of 0. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of 0. b Find Εί) and V (). c Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What is the MLE for the variance of Y?
Transcribed Image Text:3. Handin Ex. 9.84 A certain type of electronic component has a lifetime Y (in hours) with probability density function given by SO10) = { () ye-®, y > 0, otherwise. That is, Y has a gamma distribution with parameters a = 2 and 0. Let ô denote the MLE of 0. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours. a Find the MLE of 0. b Find Εί) and V (). c Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation. d What is the MLE for the variance of Y?
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