Question

find the binomial distribution for which mean is 4 and variance is 3?

Answer 1

In a binomial distribution, mean=np and variance=np(1-p) where n is the sample size or number of trials and p the probability of success.

So np=4 and np(1-p)=3, so 4(1-p)=3, 1-p=¾, p=¼, and np=4 so n=4/¼=16.

The binomial distribution is (0.25+0.75)¹⁶=0.25¹⁶+16×0.25¹⁵0.75+...+C(16,r)0.25ʳ0.75ⁿ⁻ʳ+..