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Math Help - Joint PDF explaining question

  1. #1
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    Joint PDF explaining question

    Hiya

    Got a question on joint density of two voltages:

    f(x,y) = {2, {0<x<1}and{0<y<1-x} 0, otherwise

    So I drew what I thought was f(x,y) in plan view (the region {0<x<1}and{0<y<1-x}). Is this correct?
    Next question was tow explain if the voltages x and y are independent. It seems to me that they can't be because the joint PDF depends on both x AND y, where as if they were independent it would depend on x OR y. I understand the idea of statistical independence, but not how it translates in the maths.

    Thanks very much in advance for any help.
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  2. #2
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    Re: Joint PDF explaining question

    Independence of the two rVars X,Y corresponds with F (x,y) = F_x (x) F_y (y) being true.
    That is, the random variables are said to be independent if their joint CDF factors into the product of their marginal CDF's. (ref:Rice (2007))
    So, I think you should be able to find the marginals and then do a check to see if they are indeed independent.

    (I am also learning this stuff at the moment, so don't take my word as absolute truth...)
    Last edited by howdigethere; June 7th 2012 at 12:21 AM. Reason: made to make sense
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