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Math Help - Constant R.V

  1. #1
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    Constant R.V

    If X,Y are independent and suppose P(X+Y=\alpha)=1 where \alpha is a constant. How can I show that both X and Y are constant random variables?
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  2. #2
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    Hello,

    Prove that it is not possible that :
    - X and Y have a continuous distribution
    - X or Y has a continuous distribution

    then prove that if X and Y have a discrete distribution, they necessarily are constant...

    I'm trying to find a more beautiful way to solve it
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