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November 23rd, 2010, 04:35 PM  #1 
Newbie Joined: Nov 2010 Posts: 11 Thanks: 0  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 
November 23rd, 2010, 07:31 PM  #2 
Senior Member Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14  Re: Covariance and correlation coefficient
The domain on the uv 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 
November 23rd, 2010, 08:13 PM  #3 
Senior Member Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14  Re: Covariance and correlation coefficient
I have corrected some mistakes in the above. Please have a check

November 23rd, 2010, 08:15 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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. 
November 23rd, 2010, 08:27 PM  #5 
Newbie Joined: Nov 2010 Posts: 11 Thanks: 0  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. 
November 23rd, 2010, 08:42 PM  #6  
Senior Member Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14  Re: Covariance and correlation coefficient Quote:
 
November 23rd, 2010, 09:20 PM  #7  
Senior Member Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14  Re: Covariance and correlation coefficient Quote:
 

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coefficient, correlation, covariance 
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