Question

The mean and variance of a Binomial variate are 2.4 and 1.44 respectively. Find the

parameters​

Answer 1

Answer:

Given:–

• Mean of a binomial distribution, $np = 2.4$
• Variance of a binomial distribution,$npq = 1.44$

To find:–

• The parameter values of n, p and q=?

Solution:–

Since,

Mean,np=2.4

variance,npq=1.44

Now, divide variance and mean,

$\frac{npq}{np} = \frac{1.44}{2.4}$

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

So,The value of q=0.6

As we know that,

$p + q = 1$

$p = 1 - q$

$p = 1 - 0.6$

$p = 0.4$

Now,

Mean,$np = 2.4$

$n = \frac{2.4}{0.6}$

$n = 6$

So,The parameters of a binomial distribution are p=0.4,q=0.6 and n is 6.