Question

If the sum of mean and variance of a binomial distribution is `25/9` for 5 trials, find p.

Answer 1

Mean = np,

Variance = npq

∴ np + npq = `25/9`  ....(Given)

∴ np(1 + q) = `25/9`

But n = 5,

q = 1 – p

∴ 5p(1 + 1 – p) = `25/9`

∴ 5p(2 – p) = `25/9`

∴  10p – 5p² = `25/9`

∴ 2p – p² = `5/9`

∴ 9p² – 18p + 5 = 0

∴ (3p – 5)(3p – 1) = 0

∴ p = `5/3` or p = `1/3`

But p ≤ 1

`\implies` p = `1/3`