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Joint CDF help! PLZ...

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  • Joint CDF help! PLZ...

    Hi hi frustrated with this is the joint CDF.. never saw this concept in ASM actually

    Suppose and have the joint density
    fxy = c*x*y 0<x<y<1

    Find F(0.3, 0.5)

    First we need to find c. c =8 it is all clear
    and find F(x,y). after i find out F(x,y) = 2 x^2 y^2. Then I thought F(0.3,0.5) would be 2*(0.3)^2 * (0.5)^2. but the answer is like

    So F(0.3,0.5) = 2(0.3)2 (0.5)2 - (0.3)4 = 0.045 - 0.0081 = 0.0369
    Round to .037

  • #2
    Well once you have the constant you evaluate the double integral to find the value of the CDF:

    F(X<=0.3, Y<=0.5) = S[from 0 to 0.3]S[x to 0.5](8st)dtds = S[from 0 to 0.3](s-4s^3)ds = .0369

    The inside integral is summed from x to 0.5 over t and the outside is from 0 to 0.3 over s (I realize the notation is confusing).

    In my 13th edition of the ASM, the definition was on the first page of the multivariate section.