Suppose the random variable, X, follows an exponential distribution with mean 0 (0 ≤ 0<∞). Let X₁, X₂,..., X, be a random sample of size n from the population of X. (e) If Y₁, Y₂...., Y is a random sample from another exponential distribution with mean 6, find the likelihood ratio criterion for testing Ho: 0= 6 versus H₁: 06. (Note here you need to use both samples - X₁, X2,..., X₁, and Y₁, Y2,..., Ym to test the equality of the two population means.) (f) Using the sampling distributions of 2nX and my under Ho: 0= 6, show that the above test in part (e) is based on an F statistic. [Hint: Both statistics follow x² distributions independently.]
Suppose the random variable, X, follows an exponential distribution with mean 0 (0 ≤ 0<∞). Let X₁, X₂,..., X, be a random sample of size n from the population of X. (e) If Y₁, Y₂...., Y is a random sample from another exponential distribution with mean 6, find the likelihood ratio criterion for testing Ho: 0= 6 versus H₁: 06. (Note here you need to use both samples - X₁, X2,..., X₁, and Y₁, Y2,..., Ym to test the equality of the two population means.) (f) Using the sampling distributions of 2nX and my under Ho: 0= 6, show that the above test in part (e) is based on an F statistic. [Hint: Both statistics follow x² distributions independently.]
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![Suppose the random variable, X, follows an exponential distribution with mean 0 (0 ≤
0<∞). Let X₁, X₂,..., X₁, be a random sample of size n from the population of X.
(e) If Y₁, Y2...., Ym is a random sample from another exponential distribution with
mean 6, find the likelihood ratio criterion for testing Ho: 0= 6 versus H₁ : 06.
(Note here you need to use both samples - X₁, X2, Xn and Y₁, Y2, ..., Ym to test
the equality of the two population means.)
(f) Using the sampling distributions of nX and mY under Ho: 0= 6, show that the
above test in part (e) is based on an F statistic. [Hint: Both statistics follow x²
distributions independently.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17176ae9-b253-442d-89f9-517b049b4c59%2F2b35df8d-2796-4342-b251-79f6f8ae77d7%2F1b064a_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose the random variable, X, follows an exponential distribution with mean 0 (0 ≤
0<∞). Let X₁, X₂,..., X₁, be a random sample of size n from the population of X.
(e) If Y₁, Y2...., Ym is a random sample from another exponential distribution with
mean 6, find the likelihood ratio criterion for testing Ho: 0= 6 versus H₁ : 06.
(Note here you need to use both samples - X₁, X2, Xn and Y₁, Y2, ..., Ym to test
the equality of the two population means.)
(f) Using the sampling distributions of nX and mY under Ho: 0= 6, show that the
above test in part (e) is based on an F statistic. [Hint: Both statistics follow x²
distributions independently.]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON