# Thread: Mean of a Joint Random Variable

1. ## Mean of a Joint Random Variable

I am new to statistics, so bare with me please.
I have the following question to answer.

Suppose X and Y have joint density

Find the mean of Y.

As I understand it, I need to do the following to find the mean of Y

My problem is with the limits of integration. Am I correct to assume that I need to split this double integral up into 2 double integrals and add them together? To this effect I have come up with

Is this what I want to do?

Bidski

2. ## Re: Mean of a Joint Random Variable

Your second integral doesn't quite make sense. If you're integrating with respect to x first then you shouldn't have x as one of your integration limits.

3. ## The Following User Says Thank You to Dason For This Useful Post:

Bidski (08-23-2012)

4. ## Re: Mean of a Joint Random Variable

Oops, sorry. That part is a typo. It should be dydx for the second double integal.

5. ## Re: Mean of a Joint Random Variable

Ah - then it looks good to me.

6. ## The Following User Says Thank You to Dason For This Useful Post:

Bidski (08-23-2012)

7. ## Re: Mean of a Joint Random Variable

Cool, thanks for the confirmation.

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