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!
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Hey alphabeta89. To start off with: what did you get for your region of integration?
Originally Posted by chiro Hey alphabeta89. To start off with: what did you get for your region of integration? -y<x<y, 0<y<\infty
Hint: Integrate out the x variable first and use the properties of the Gamma Function: Gamma function - Wikipedia, the free encyclopedia
Do we need to find out what is ? Then use ?
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.
Hi, just to check, is this correct?
Can you show the step by step integration techniques to get f_y(Y)? The steps and approach look good.
Originally Posted by chiro Can you show the step by step integration techniques to get f_y(Y)? The steps and approach look good. . Is this correct?
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.
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