# Math Help - Mode of Poisson distribution

1. ## 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!

2. Originally Posted by jlt1209
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 $\displaystyle \frac{\lambda}{n} > 1$.