If X has a binomial distribution, B(n, p) with parameters n and p such that P(X=2)=P(X=3) , then E ( X ) , the mean of variable X , is

Step-by-step solution

Since X has a binomial distribution, B (n , p) aligned & P (X=2)= ^n C ₂(p)^2(1-p)^ n-2 & and P (X=3)= ^n C ₃(p)^3(1-p)^ n-3 & Given P (X=2)= P (X=3) & ^n C ₂ p^2(1-p)^ n-2 = ^n C ₃(p)^3(1-p)^ n-3 & n ! 2 !(n-2) ! p^2(1-p)^n (1-p)^2 &= n ! 3 !(n-3) ! p^3(1-p)^n (1-p)^3 aligned aligned & 1 n-2 = 1 3 p 1-p & 3(1-p)=p(n-2) & 3-3 p=n p-2 p & n p=3-p & E (X)= mean =3-p &( mean of B (n, p)=n p) aligned