Suppose has a binomial distribution . Show that is the most likely outcome. (Hint: is the maximum among all )
Suppose has a binomial distribution . Show that is the most likely outcome. (Hint: is the maximum among all )

Solution:

Given is any random variable whose binomial distribution is

Thus, and

Thus, , where

It can be clearly observed that will be maximum if will be maximum.

Hence we can clearly see that is maximum.

for is maximum.

Hence, proved that the most likely outcome is .