Question

The probability that a patient recovers from a rare blood disease is 0.4. If 15 people are known to have contracted this disease.

Find the mean and variance of the binomial random variable?

Answer 1

The probability that patient recovers from a rae blood diesease is 0.4

Hence, p = 0.4 ,

there are 15 people who contracted the disease, so ,n=15

We know that q= 1-p= 1 - 0.4 = 0.6

So n=15, p= 0.4 , q=0.6 ,and it is said that it follows binomial distribution.

So, mean in binomial distribution = n*p

Mean= 15 * 0.4 = 6

Variance in binomial distrbution = n*p*q=n*p*(1-p)

Variance = 15*0.4*0.6=3.6

Therefore , mean and variance of binomial random variable are 6 and 3.6 respectively.