Question

If the mean and variance of a binomial variable X are 2.4 and 1.44 respectively, find the perimeters of the distribution X. (Binomial)

Answer 1

Given:-

Mean $=2.4$

Variance $=1.44$

As we know that mean and variance of a binomial distribution is given as-

Mean $=np$

Variance $=npq$

Therefore,

$np=2.4.....\left(1\right)$

$npq=1.44.....\left(2\right)$

From equation $\left(1\right)\&\left(2\right)$, we have

$q=\frac{1.44}{2.4}=0.6$

Therefore,

$p=1-q=1-0.6=0.4$

Substituting the value of $p$ in equation $\left(1\right)$, we have

$n=\frac{2.4}{0.4}=6$

Hence the perimeters of the binomial distribution $X$ are-

$n=6$

$p=0.4$

$q=0.6$