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Math Help - Joint distribution

  1. #1
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    Joint distribution

    I am given X has distribution f(x)= (1/σ)*e^(-x/σ) and Y has the same distribution but with μ and y in place of sigma and x. I am also given Z=min{X,Y} and W={1 if Z=X and 0 if Z=Y}.
    I am told to find the joint distribution of Z and W and also prove Z and W are independent.
    I am stuck on this one. Does it break down into two cases (Z=X and Z=Y)?
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  2. #2
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    Quote Originally Posted by kman320 View Post
    I am given X has distribution f(x)= (1/σ)*e^(-x/σ) and Y has the same distribution but with μ and y in place of sigma and x. I am also given Z=min{X,Y} and W={1 if Z=X and 0 if Z=Y}.
    I am told to find the joint distribution of Z and W and also prove Z and W are independent.
    I am stuck on this one. Does it break down into two cases (Z=X and Z=Y)?
    kman320,

    Are you sure of your problem statement? It looks to me like Z and W are dependent.
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  3. #3
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    Its seems they are, but he gives a hint. Show the prob. that Z<z given W=i (for i=1,2) is equal to the prob. Z<z.
    Show P(Z<z l W=i)=P(Z<z) .
    How will I go about doing the first step of finding the joint dist. of Z & W?
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  4. #4
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    Anyone?
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