The mean and variance of a binomial distribution are 5 and 4 respectively. Then what is p(X=1)= ?

Step-by-step solution

Mean of binomial distribution =5 Variance of binomial distribution =4 n p=5 and n p q=4 Use n p=5 in n p q=4 , we get (5)q q q=4 / 5 Now, p=1-q=1- 4 5 = 1 5 Given n p=5 n= 5 p =25 [ p=1 / 5] aligned P(X=1) & = ²⁵ C₁ p^x q^ n-x & = ²⁵ C₁ ( 1 5 ) ( 4 5 )²⁴ & = 25 5 ( 4 5 )²⁴=5 4²⁴ 5²⁴ P(X=1) & = 4²⁴ 5²³ aligned