If a random variable (x) follows binomial distribution with mean 5 and variance 4 , and 5 ²³ P ( X =3)= 4^ , then what is the value of ?

Step-by-step solution

gathered Mean =5 and variance =4 5²³ P ( X =3)= 4^ ...(i) gathered aligned & Mean & =5 & n p & =5 & Variance & =4 & n p q & =4 & 5 q & =4 & q & = 4 5 aligned Now, p=1-q=1- 4 5 = 1 5 aligned & n p & =5 & n & =25 aligned Now, 5²³ P ( X =3)=5²³ [n c^3 p^3 q^ n-3 ] aligned & =5²³ [ ²⁵ C ₃ ( 1 5 )^3 ( 4 5 )²² ] & =5²³ [ 25 24 23 6 1 5^3 4²² 5²² ] & =4 23 4²² aligned 5²³ P ( X =3)=23 4²² ....(ii) From (i) and (ii) =23