If X follows a binomial distribution with parameters `n=100 and p = 1/3`, then `P(X = r)` is maximum when

Explanation

`P(X = r) ` will be maximum when r is the mode

`therefore` There are two cases for mode of Binomial Distribution which are as follows:

`Case 1:` If `(n+1)p` is an integer the Binomial Distribution is bimodal and the two modal value will be `(n+1)p and (n+1)p-1`

`Case 2:` If `(n+1)p` is not an integer there exists unique modal value and it’s the integral part of `(n+1)p` .

The given Binomial Distribution has parameters, `n=100` and `p=1/3`.

`therefore` We have `(n+1)p = (100+1)/3 = 101/3 = 33.67`, which is not an integer

Hence, the unique mode is 33, which is the integral part of `(n+1)p`.

`therefore`, `P(X=r)` will be maximum when `r = 33`