Question

The mean and variance, respectively, of a binomial distribution for n independent trials with the probability of success as p, are
1. \(\sqrt {np},\;\sqrt {np(1 - p)}\)
2. \(\sqrt {np},\) np (1 - 2p)
3. np, np(1 - p)
4. np, np

Answer 1

Correct Answer - Option 3 : np, np(1 - p)

Explanation:

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

P(X = k) = \(\rm ^nC_kp^kq^{n-k}\)

where n is the number of observations, p is the probability of success & q is the probability of failure.p nCkpkqn−knCkpkqn−k

Total probability, p + q = 1

q = 1 - p

Mean = np 

Variance = npq = np(1 - p)