Question

If X has a binomial distribution with n = 20 , p = `1/10` , find E (X) and V (X).

Answer 1

Given X ~  B(n, p) 

Where n = 20 , p = `1/10`

P + q = 1

∴ q = 1 - p = `1-1/10 = 9/10`

∴ n = 20 , p = `1/10` , q = `9/10`

Mean= E(x) = np =`20 xx 1/10 = 2`

Variance = V(x) = npq = `20 xx 1/10 xx 9/10`

`= 18/10 = 1.8`