1. Suppose we are interested in investigating the lifespan of a Texas Instrument calculator and we model the lifespan using an exponential distribution with unknown parameter (X). If we test 5 calculators, and their lifetimes are 2, 3, 1, 3, and 4 years, respectively, (a) What is the maximum likelihood estimator for X? (b) What does it mean in words?
1. Suppose we are interested in investigating the lifespan of a Texas Instrument calculator and we model the lifespan using an exponential distribution with unknown parameter (X). If we test 5 calculators, and their lifetimes are 2, 3, 1, 3, and 4 years, respectively, (a) What is the maximum likelihood estimator for X? (b) What does it mean in words?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![1. Suppose we are interested in investigating the lifespan of a Texas Instrument calculator
and we model the lifespan using an exponential distribution with unknown parameter
(A). If we test 5 calculators, and their lifetimes are 2, 3, 1, 3, and 4 years, respectively,
(a) What is the maximum likelihood estimator for X?
(b) What does it mean in words?
2. Say we are given a table representing the bivariate probability mass function f(X,Y)
X = 1
X = 2
X = 3
Y = 1 Y = 2
0
1/8
0
0
1/4
0
Y = 3
3/8
1/4
0
Find P(Y=2|X = 1)
3. We are given the following bivariate density function :
f(x,y) = y ( ²2 − x).
-
where X and Y represent the lifespan of two electrical components in a transistor.
(a) Check that f(x, y) is actually a bivariate density
(b) Find the marginal pdfs, f(x) and f(y)
+x; where 0<x< 1 and 0 < y < 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe19ec3d8-d861-4c74-a362-426e6d561991%2F6a7f0670-3026-4bc1-9336-38d355a1e93d%2Fmc0h36f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose we are interested in investigating the lifespan of a Texas Instrument calculator
and we model the lifespan using an exponential distribution with unknown parameter
(A). If we test 5 calculators, and their lifetimes are 2, 3, 1, 3, and 4 years, respectively,
(a) What is the maximum likelihood estimator for X?
(b) What does it mean in words?
2. Say we are given a table representing the bivariate probability mass function f(X,Y)
X = 1
X = 2
X = 3
Y = 1 Y = 2
0
1/8
0
0
1/4
0
Y = 3
3/8
1/4
0
Find P(Y=2|X = 1)
3. We are given the following bivariate density function :
f(x,y) = y ( ²2 − x).
-
where X and Y represent the lifespan of two electrical components in a transistor.
(a) Check that f(x, y) is actually a bivariate density
(b) Find the marginal pdfs, f(x) and f(y)
+x; where 0<x< 1 and 0 < y < 2
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1: Introduction to problem
We have been provided with the lifespan of 5 different TI-calculators having IID exponential distribution.
We need to find the MLE and interpret it with respect to question.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
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](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman