# Poisson distribution problem

• Oct 2nd 2013, 12:48 AM
Nora314
Poisson distribution problem
Hi all, hope you are having a fine day :)

My problem is:

Let X and Y be independent Poisson distributed stochastic variables, with expectation values
5 and 10, respectively. Calculate the following probabilities:

X + Y > 10

What I have done to solve it:

I found the Poisson probabilities when r = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 for both X and Y, then I added them all together, and subtracted them from 1. I keep getting the wrong answer, and my answer is over 1, which is a bit strange. The answer key says the correct answer should be: 0,882

Thanks!
• Oct 2nd 2013, 01:37 AM
chiro
Re: Poisson distribution problem
Hey Nora314.

Hint: Write down all possible pairs of values where X + Y <= 10 and use the fact that P(A = a, B = b) = P(A=a)*P(B=b) for independent random variables A and B (with corresponding events a and b respectively).

To keep track of things, I suggest you write the pairs with the corresponding probability.

After this, you should be able to get the final answer.