In a binomial distribution, the difference between the mean and standard deviation is 3 and the difference between their squares is 21 , then P (x=1): P (x=2)=

Step-by-step solution

Mean =n p Standard deviation = 2 p(1-p) According to question, n p- n p(1-p) =3 aligned & n p-3= n p(1-p) & (n p-3)^2=n p(1-p) ....(i) aligned And, aligned & n^2 p^2-n p(1-p)=21 & n p(1-p)=n^2 p^2-21 ....(ii) aligned From (i) or (ii), (n p-3)^2=n^2 p^2-21 9-6 n p=-21 n p=5 Put in (ii), 5(1-p)=25-21 p= 1 5 and n=25, q= 4 5 P(X=1) P(X=2) = ²⁵ C₁ p q²⁴ ²⁵ C₂ p^2 q²³ = 1 12 q p = 1 3