The binomial distribution of a random variable X is given by, P(X=k)=nCkpkqn−k Mean =np Variance =npq Given, the mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, ⇒mean =np=4 ⇒ variance =npq=2 From equation (1) and (2), we have ⇒q=
1
2
We know, p=1−q ⇒p=
1
2
From equation (1), we have n=8 The binomial distribution of a random variable X is given by, P(X=k)=nCkpkqn−k ⇒P(X=1)=8C1p1q8−1 ⇒P(X=1)=8⋅