## The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is

Solution : Given that, for binomial distribution mean, np = 4 and variance, npq = 2. \(\therefore\) q = 1/2, but p + q = 1 \(\implies\) p = 1/2 and n \(\times\) \(1\over 2\) = 4 \(\implies\) n = 8 We know that, P(X = r) = \(^nC_r p^r q^{n-r}\) \(\therefore\) P(X = 1) …