1. ## Poisson

If X~Po(2) and Y~Po(1). How to find P(X>Y)?

2. Originally Posted by syjytg
If X~Po(2) and Y~Po(1). How to find P(X>Y)?
Are X and Y independent?

3. Yes, X and Y are independent.

4. Originally Posted by syjytg
Yes, X and Y are independent.
The joint pdf is $f(k, l) = \left( \frac{e^{-2} 2^k}{k!} \right) \, \left( \frac{e^{-1} 1^l}{l!} \right) = \frac{e^{-3} 2^k}{k! \, l!}$.

$\Pr(X > Y) = \sum_{k=1}^{\infty} f(k, 0) + \sum_{k=2}^{\infty} f(k, 1) + \sum_{k=3}^{\infty} f(k, 2) + \, ....$

5. Can you please complete it until you get the answer? I still do not know how to continue from here.

I mean I do not know how to evaluate the expression you gave above.