Homework Help is Here – Start Your Trial Now!
Math
Statistics
Using [Hint_1] show that the sampling distribution of MLE is given by OMLE 0 N Fn-1m-1 i.e., the sampling distribution of MLE is an F distribution with n - 1 degrees of freedom in the numerator, and m - 1 degrees of freedom in the denominator.

Using [Hint_1] show that the sampling distribution of MLE is given by OMLE 0 N Fn-1m-1 i.e., the sampling distribution of MLE is an F distribution with n - 1 degrees of freedom in the numerator, and m - 1 degrees of freedom in the denominator.

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

I want to know the answer and details step by step

Thank you so much

In this question, we will set up and test the appropriate hypothesis for verifying a claim from astronomy. • The Bubble space telescope is an optical telescope that was launched into space in 1990 to collect data from distant stars and glaxies, and has proven to be an invaluable source of information to many astronomers and cosmologists. • Recently, a team of researchers from NASA led the design and development of the Webb space telescope, which was claimed to be capable of higher resolution images and less error-prone in comparison to its predecesor, the Bubble space telescope. • In order to lend credence to the claim that the newly designed Webb space telescope was capable of more accurate measurements compared to the Bubble space telescope, the scientists from NASA were required to show sufficient evidence for this claim in a formal statistical setting. In order to test the hypothesis that the measurement error from the Webb telescope was indeed smaller than the measurement error from the Bubble telescope, the researchers designed the following experiment: A collection of n and m observations were taken of a fixed object in the observable universe by, the Bubble telescope and the Webb telescope, respectively. Let X1, X2,..., X, N(μ, ox) denote the collection of n observations taken by the Bubble Telescope, and let Y₁, Y2,..., Ymd N(μ, o) denote the collection of n observations taken by the Webb Telescope. The mean μ is the true (unknown) brightness of the object, and the (unknown) variances o and o represent the measurement error from the Bubble and Webb telescopes, respectively. Using this information, answer the following questions. [Hint 1] In class, we saw that if we are given two random variables X~X and Y~ x the distribution of (X/n)/(Y/m) is given by Also, in the midterm we saw that X/n Y/m Fnm T (k, 2) = X₂k¹ i.e., A Gamma distribution with parameters (k, 2) is a Chi-squared distribution with 2k degrees of freedom. Similarly, if c> 0 is some constant then cX~ I (a₁, c), i.e., multiplying a Gamma distribution by c results in a new Gamma distribution with the same shape a₁ but the scale becomes cß.
Transcribed Image Text:In this question, we will set up and test the appropriate hypothesis for verifying a claim from astronomy. • The Bubble space telescope is an optical telescope that was launched into space in 1990 to collect data from distant stars and glaxies, and has proven to be an invaluable source of information to many astronomers and cosmologists. • Recently, a team of researchers from NASA led the design and development of the Webb space telescope, which was claimed to be capable of higher resolution images and less error-prone in comparison to its predecesor, the Bubble space telescope. • In order to lend credence to the claim that the newly designed Webb space telescope was capable of more accurate measurements compared to the Bubble space telescope, the scientists from NASA were required to show sufficient evidence for this claim in a formal statistical setting. In order to test the hypothesis that the measurement error from the Webb telescope was indeed smaller than the measurement error from the Bubble telescope, the researchers designed the following experiment: A collection of n and m observations were taken of a fixed object in the observable universe by, the Bubble telescope and the Webb telescope, respectively. Let X1, X2,..., X, N(μ, ox) denote the collection of n observations taken by the Bubble Telescope, and let Y₁, Y2,..., Ymd N(μ, o) denote the collection of n observations taken by the Webb Telescope. The mean μ is the true (unknown) brightness of the object, and the (unknown) variances o and o represent the measurement error from the Bubble and Webb telescopes, respectively. Using this information, answer the following questions. [Hint 1] In class, we saw that if we are given two random variables X~X and Y~ x the distribution of (X/n)/(Y/m) is given by Also, in the midterm we saw that X/n Y/m Fnm T (k, 2) = X₂k¹ i.e., A Gamma distribution with parameters (k, 2) is a Chi-squared distribution with 2k degrees of freedom. Similarly, if c> 0 is some constant then cX~ I (a₁, c), i.e., multiplying a Gamma distribution by c results in a new Gamma distribution with the same shape a₁ but the scale becomes cß.
5. Using [Hint_1] show that the sampling distribution of MLE is given by OMLE 0 Fn-1,m-1 i.e., the sampling distribution of MLE is an F distribution with n 1 degrees of freedom in the numerator, and m - 1 degrees of freedom in the denominator. By fixing the Type-l error probability to be equal to cx, i.e., a = P(Type-I Error) derive an expression for the rejection region R(0; a) in terms of Fn-1,m-1;a, the a quantile of the Fn-1,m-1 distribution from part#5
Transcribed Image Text:5. Using [Hint_1] show that the sampling distribution of MLE is given by OMLE 0 Fn-1,m-1 i.e., the sampling distribution of MLE is an F distribution with n 1 degrees of freedom in the numerator, and m - 1 degrees of freedom in the denominator. By fixing the Type-l error probability to be equal to cx, i.e., a = P(Type-I Error) derive an expression for the rejection region R(0; a) in terms of Fn-1,m-1;a, the a quantile of the Fn-1,m-1 distribution from part#5
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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