If X is a binomial variable with range 0,1,2,3,4 and P(X=3)=3 P(X=4) then the parameter ' p ' of the binomial distribution is

Step-by-step solution

Given the binomial variable range 0,1,2,3,4 , the number of trials is n = 4 . The condition P(X = 3) = 3P(X = 4) applied to the binomial mass function P(X = k) = 4 k p^k (1-p)^ 4-k leads to the equation: 4p^3(1 - p) = 3p^4 Assuming p eq 0 , divide both sides by p^3 to obtain: 4(1 - p) = 3p Solving gives 4 = 7p and p = 4 7 . This corresponds to option D. Final Answer: D