# Math Help - Poisson Distribution Probability

1. ## Poisson Distribution Probability

I'm trying to find an expression for the probability that Y is an odd number for the Poisson distribution.

I know that it is e^-lambda * sum(lambda^y / y!) for y = 1, 3, 5, ...

But is there a way to write this such that it isn't an infinite sum?
Someway to write it without "y"?
Any hint in the right direction would be very much appreciated.

2. ## Re: Poisson Distribution Probability

Originally Posted by Relmiw
I'm trying to find an expression for the probability that Y is an odd number for the Poisson distribution.

I know that it is e^-lambda * sum(lambda^y / y!) for y = 1, 3, 5, ...

But is there a way to write this such that it isn't an infinite sum?
Someway to write it without "y"?
Any hint in the right direction would be very much appreciated.
OK, a hint: Consider the power series for sinh(x).

3. ## Re: Poisson Distribution Probability

Thanks, that helped a lot