Question

The mean and variance of a binomial distribution are 4 and 4/3 respectively.Find the p(x 3)

Answer 1

Heya,

we know

mean of a binomial distribution = np

and, variance = npq

Given, np = 4

npq = 4/3.

dividing , we get

$\frac{np}{npq} = \frac{4}{ \frac{4}{3} } \\ = > q = \frac{1}{3} \\ = > p = 1 - q \\ = > p = 1 - \frac{1}{3} = \frac{2}{3}$

Hence,

$np = 4 \\ = > n \times \frac{2}{3} = 4 \\ = > n = 6$

Hence, P(x=3) = nC3(p)³(q)³

= 6C3 (2/3)³(1/3)³

=160/729 Ans.

Regards

Kshitij