Homework Help is Here – Start Your Trial Now!
Math
Statistics
A mass-production line manufactures electrical heating elements with lifespans X; which have independent exponential distributions with pdf exp I; > 0. A sample of n elements is to be tested. If Y is the lifespan of the first of the n elements to fail, it can be shown that the pdf of Y is s0) - () e exp y > 0. (a) Use integration to show that the mean lifespan X; is 0, and the variance is 6. (b) Show that the sample mean X = D X; is an unbiased estimator of 0. (c) By noting the similarity between f(x;) and g(y) or otherwise, deduce the mean and variance of Y. (d) Find the constant k such that kY is an unbiased estimator of 0. Is the estimator consistent? (e) Which of the two estimators, X or kY, would you prefer?

A mass-production line manufactures electrical heating elements with lifespans X; which have independent exponential distributions with pdf exp I; > 0. A sample of n elements is to be tested. If Y is the lifespan of the first of the n elements to fail, it can be shown that the pdf of Y is s0) - () e exp y > 0. (a) Use integration to show that the mean lifespan X; is 0, and the variance is 6. (b) Show that the sample mean X = D X; is an unbiased estimator of 0. (c) By noting the similarity between f(x;) and g(y) or otherwise, deduce the mean and variance of Y. (d) Find the constant k such that kY is an unbiased estimator of 0. Is the estimator consistent? (e) Which of the two estimators, X or kY, would you prefer?

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
See similar textbooks
icon
Related questions
Question

answer last 3 subparts.

A mass-production line manufactures electrical heating elements with lifespans X; which have independent exponential distributions with pdf 1 exp T; > 0. (2). A sample of n elements is to be tested. If Y is the lifespan of the first of the n elements to fail, it can be shown that the pdf of Y is g(2) = , exp () y > 0. (a) Use integration to show that the mean lifespan X; is 0, and the variance is 0. (b) Show that the sample mean X = X; is an unbiased estimator of 0. (c) By noting the similarity between f(x:) and g(y) or otherwise, deduce the mean and variance of Y. (d) Find the constant k such that kY is an unbiased estimator of 0. Is the estimator consistent? (e) Which of the two estimators, X or kY, would you prefer? 2.
Transcribed Image Text:A mass-production line manufactures electrical heating elements with lifespans X; which have independent exponential distributions with pdf 1 exp T; > 0. (2). A sample of n elements is to be tested. If Y is the lifespan of the first of the n elements to fail, it can be shown that the pdf of Y is g(2) = , exp () y > 0. (a) Use integration to show that the mean lifespan X; is 0, and the variance is 0. (b) Show that the sample mean X = X; is an unbiased estimator of 0. (c) By noting the similarity between f(x:) and g(y) or otherwise, deduce the mean and variance of Y. (d) Find the constant k such that kY is an unbiased estimator of 0. Is the estimator consistent? (e) Which of the two estimators, X or kY, would you prefer? 2.
Expert Solution
steps

Step by step

Solved in 2 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Integers
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS