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Math Help - Poisson Distribution Probability

  1. #1
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    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.
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  2. #2
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    Re: Poisson Distribution Probability

    Quote Originally Posted by Relmiw View Post
    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).
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  3. #3
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    Re: Poisson Distribution Probability

    Thanks, that helped a lot
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