Question

If the sum of mean and variance of a Binomial Distribution is 4.8 for 5 trials find the distribution.

Answer 1

np + npq = 4.8 ⇒ np (1 + q) = 4.8 

5p [1 + (1 – p)] = 4.8 

p² – 2p + 0.96 = 0 ⇒ p = 1.2, 0.8 

∴ p = 0.8 ; q = 0.2 [∵ p cannot be greater than 1] 

∴ The Binomial distribution is P[X = x] = 5C_x (0.8)^x

(0.2)^{5 - x}, x = 0 to 5