If a random variable X follows the Binomial distribution B(33, p) such that 3 P(X=0)=P(X=1) , then the variance of X is

Step-by-step solution

A binomial random variable X with parameters n=33 and unknown p has its probability mass function defined as P(X=k) = n k p^k (1-p)^ n-k . The given condition 3P(X=0) = P(X=1) leads to the equation 3(1-p)³³ = 33p(1-p)³² . Since p The variance of a binomial distribution is Var (X) = np(1-p) . Substituting n=33 and p= 1 12 gives Var (X) = 33 1 12 11 12 = 363 144 = 121 48 . Final answer: 121 48