Answer :

Solution :

The binomial distribution of a random variable X is given by,

P(X = k) = ${}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{k}}{\mathrm{p}}^{\mathrm{k}}{\mathrm{q}}^{\mathrm{n}-\mathrm{k}}$

where n is the number of observations, p is the probability of success & q is the probability of failure.

${}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{k}}{\mathrm{p}}^{\mathrm{k}}{\mathrm{q}}^{\mathrm{n}-\mathrm{k}}$

Total probability, p + q = 1

q = 1 - p

Mean = np

Variance = npq = np(1 - p)