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3. A certain type of electronic component has a lifetime Y (in hours) with probability density function given by f(x; 8) = )xe, x>0 хе elsewhere 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 E(Ô) and V (ô) c. Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation.

3. A certain type of electronic component has a lifetime Y (in hours) with probability density function given by f(x; 8) = )xe, x>0 хе elsewhere 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 E(Ô) and V (ô) c. Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation.

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. A certain type of electronic component has a lifetime Y (in hours) with probability density function given by f(x; 0) =- )xe, x>0 хе elsewhere 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 E(Ô) and V(Ô) c. Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation.
Transcribed Image Text:3. A certain type of electronic component has a lifetime Y (in hours) with probability density function given by f(x; 0) =- )xe, x>0 хе elsewhere 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 E(Ô) and V(Ô) c. Suppose that 0 actually equals 130. Give an approximate bound that you might expect for the error of estimation.
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