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Joint probability,-limit values

  1. Nov 1, 2009 #1
    hello
    i have given this problem to find pdf of function z.i have solved most of it and stuck at the end.
    i have attached problem and my solution so far as pdf here.
    what i want to know what are the integral limits for finding f(z) using marginal density (see the end the end of attached solution is it [0 to z] or [z to 1] ?)

    thanks.
     

    Attached Files:

  2. jcsd
  3. Nov 3, 2009 #2
    start with
    P(Z<=z)
    =P(XY<=z)
    =P(Y<=z/x), x not equals 0
    from here we do double integration on pxy(x,y) to obtain area of Fxy(Y<=z/x)=1-P(Y>z/x)=Fz
    The limit of x is from z to 1, limit of y is z/x to 1

    Fz(z) my calculation z^2-2zlnz
     
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