In a binomial distribution, the sum and the product of the mean and the variance are (25/3) and (50/3) respectively. Find the distribution.
Mean + Variance = np + npq = np(1 + q) = 25/3
Variance = n2p2q = n2 = 50/3 …(i)
n2p2(1 + q)2 = 625/9 …(ii)
Dividing (i) by (ii), we get,
⇒ 6q2-13q + 6 = 0
⇒ q = 2/3 or 3/2
⇒ But as q can not be greater than 1 thus, q = 2/3.
⇒ p = 1/3
⇒ n = 15
Binomial distribution,
1