The joint density function of X and Y is given by

, where .

Find .

How do I go about doing this question? Any help is appreciated. Thanks in advance!(Happy)

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- Jan 2nd 2013, 10:09 PMalphabeta89finding expectation
The joint density function of X and Y is given by

, where .

Find .

How do I go about doing this question? Any help is appreciated. Thanks in advance!(Happy) - Jan 2nd 2013, 10:29 PMchiroRe: finding expectation
Hey alphabeta89.

To start off with: what did you get for your region of integration? - Jan 2nd 2013, 11:15 PMalphabeta89Re: finding expectation
- Jan 3rd 2013, 12:12 AMchiroRe: finding expectation
Hint: Integrate out the x variable first and use the properties of the Gamma Function:

Gamma function - Wikipedia, the free encyclopedia - Jan 3rd 2013, 07:33 AMalphabeta89Re: finding expectation
Do we need to find out what is ? Then use ?

- Jan 3rd 2013, 02:45 PMchiroRe: finding expectation
You could find the conditional distribution or you could just condition Y on the appropriate values and get the expectation.

They will both give you the same result and the rigorous way to prove it is to use Fubini's Theorem. - Jan 4th 2013, 07:41 AMalphabeta89Re: finding expectation
Hi, just to check, is this correct?

- Jan 4th 2013, 05:36 PMchiroRe: finding expectation
Can you show the step by step integration techniques to get f_y(Y)?

The steps and approach look good. - Jan 5th 2013, 11:19 PMalphabeta89Re: finding expectation
- Jan 5th 2013, 11:37 PMchiroRe: finding expectation
That looks right algebraically.

One way to confirm the theoretical results is to simulate the random variables in a statistical package if you so choose to do.