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Sample Distribution Question

  • #1

Homework Statement



[PLAIN]http://img40.imageshack.us/img40/1503/question1l.jpg [Broken]

Homework Equations



[URL]http://onlinecourses.science.psu.edu/stat414/sites/onlinecourses.science.psu.edu.stat414/files/lesson26/Variance10.gif[/URL]

[URL]http://onlinecourses.science.psu.edu/stat414/sites/onlinecourses.science.psu.edu.stat414/files/lesson26/Variance11.gif[/URL]

[URL]http://onlinecourses.science.psu.edu/stat414/sites/onlinecourses.science.psu.edu.stat414/files/lesson26/Variance13.gif[/URL]

The Attempt at a Solution



I need help with this question. I know that to get this distribution, I need to sum the Z^2's of both respective samples. However, in order to do so wouldn't I need to prove that Z^2's are independent? I'm assuming I'll need to utilize the moment generating function. However, I'm not sure how to go about this. Any help would be much appreciated!

Homework Statement





Homework Equations





The Attempt at a Solution

 
Last edited by a moderator:

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
so if you're happy up to the point where Z^2 is equivalent to chi square distribution with 1 DoF, then the sum of two chi square distribution with DoF k1 & k2 is another chi square distribution with DoF = k1 + k2.

the question says the 2 samples are independent. As it is not stated otherwise I would assume the individual samples are independent, though state it as a n assumption
 

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