The variance of a binomial random variable for n trials and

The variance of a binomial random variable for n trials, and probability of success p is np(1-p). What is the value of p that gives the highest variance

Solution

Variance of B(n,p) is np(1-p).

When p = 1/2, Variance = n(1/2)(1/2) = 1/4.

The maximum value of the variance is n/4 when p=1/2, and the minimm value is 0 when p=0 or p=1.