Question

In binomial distribution, the sum and the product of mean and the variance are $\frac{25}{3}$ and $\frac{50}{3}$ respectively. Determine the distribution.

Answer 1

Mean $=np$

Variance $=npq$

$np+npq=\frac{25}{3}$

$n^2{p}^{2}q=\frac{50}{3}$

Also $q=1-p$

on solving we get

$n=15p=\frac{1}{3}q=\frac{2}{3}$

$B$ in rational distribution is at $15$ distribute trails in which probability of success $=\frac{1}{3}$