1. ## 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?

2. 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