Question

A random variable $X$ is binomial distributed with mean $12$ and variance is $8$. Find the parameter of the distribution are

• A. $18,\frac{1}{3}$
• B. $36,\frac{1}{3}$
• C. $36,\frac{2}{3}$
• D. $18,\frac{2}{3}$

Answer 1

The correct option is B $36,\frac{1}{3}$

Solution -

Mean = np = 12

Variance = npq = 8

then q = 1 - p

$\frac{npq}{np}=\frac{8}{12}$ $q=\frac{2}{3}$

$p=1-\frac{2}{3}=\frac{1}{3}$

$n\times \frac{1}{3}=12$

$n=36$

$36,\frac{1}{3}$

B is correct