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Math Help - Mode of Poisson distribution

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    Mode of Poisson distribution

    Find the mode of a P(lamda) distribution.

    I believe that where lamda is not an integer, the mode is floor(lamda) (largest integer <= lamda) and where lamda is a positive integer, the mode is lamda and lamda-1, but can someone help explain how to get to this point ... I can't seem to figure out how to get to these values.

    Thank you!
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    Quote Originally Posted by jlt1209 View Post
    Find the mode of a P(lamda) distribution.

    I believe that where lamda is not an integer, the mode is floor(lamda) (largest integer <= lamda) and where lamda is a positive integer, the mode is lamda and lamda-1, but can someone help explain how to get to this point ... I can't seem to figure out how to get to these values.

    Thank you!
    Hint: \displaystyle \frac{\lambda^n}{n!} \geq \frac{\lambda^{n-1}}{(n-1)!} provided \displaystyle \frac{\lambda}{n} > 1.
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