Question on Binomial distribution maximum at n.

Jul 2015
564
14
United States
For which values of P will the p.m.f. of the Bin(n,p) distribution have its maximum at n?

I suspect low values of p will have its maximum at n.

How can I prove this? I can show you a specific example, such as rolling a die 10 times, p=1/6. But that is just a specific example.
 

romsek

MHF Helper
Nov 2013
6,647
2,994
California
consider looking at the ratio of adjacent values of k.
same thing with your Poisson distribution problem.