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November 23rd, 2010, 04:35 PM   #1
knp
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Covariance and correlation coefficient

Hi all,

If anybody knows how to work with joint probability function of multiple random variables, please take a look at this problem and see if you can give me any pointers.

I know you first need to find the marginal pdf of both U and V to get their respective means and variances. Then you need to find the expected value of X and Y (EXY) by double integration. Following, you use all the obtained results in the covariance formula in the second attachment below.

Then finally, you use the obtained covariance of X and Y to find the correlation coefficient in the third attachment below.

I hope my explanation is somewhat clear.

What I need help with is the mechanics of the problem. Is anybody familiar?

Thanks for looking.

knp
Attached Images
File Type: jpg Correlation Coefficient.jpg (9.5 KB, 160 views)
File Type: jpg Covariance.jpg (10.6 KB, 160 views)
File Type: jpg C and CC.jpg (18.1 KB, 160 views)
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November 23rd, 2010, 07:31 PM   #2
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Re: Covariance and correlation coefficient

The domain on the u-v plane is shown as the following:

[attachment=0:238ndci0]1.JPG[/attachment:238ndci0]

As the joint probability function is



the marginal probability functions are



.

Use (ii) and (iii), the expectations are





Also, the variances are





And the covariance is



The correlation cofficient is

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File Type: jpg 1.JPG (7.3 KB, 151 views)
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November 23rd, 2010, 08:13 PM   #3
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Re: Covariance and correlation coefficient

I have corrected some mistakes in the above. Please have a check
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November 23rd, 2010, 08:15 PM   #4
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Re: Covariance and correlation coefficient

I vaguely thought the correlation coefficient should be 0 < r ? 1, but I wasn't gonna question you, when I wasn't sure.
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November 23rd, 2010, 08:27 PM   #5
knp
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Re: Covariance and correlation coefficient

I'm not quite sure how you obtained 0.7071 for the correlation coefficient. Am I missing something here? The rest of the problem looks great.
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November 23rd, 2010, 08:42 PM   #6
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Re: Covariance and correlation coefficient

Quote:
Originally Posted by knp
I'm not quite sure how you obtained 0.7071 for the correlation coefficient. Am I missing something here? The rest of the problem looks great.
the standard deviation , this is from my text book
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November 23rd, 2010, 09:20 PM   #7
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Re: Covariance and correlation coefficient

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Originally Posted by MarkFL
I vaguely thought the correlation coefficient should be 0 < r ? 1, but I wasn't gonna question you, when I wasn't sure.
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