A random variable X assumes values 1,2,3, ., n with equal probabilities. If var (X): E(X)=4: 1 , then n is equal to

Step-by-step solution

According to the given condition, probability distribution function is E(X)= 1+2+ +n n = n(n+1) 2 n = n+1 2 aligned E (X^2 )= 1^2+2^2+ +n^2 n & = n(n+1)(2 n+1) 6 n & = (n+1)(2 n+1) 6 aligned aligned Var (X) & =E (X^2 )-[E(X)]^2 & = (n+1)(2 n+1) 6 - (n+1)^2 4 & = 2 n^2+3 n+1 6 - n^2+2 n+1 4 & = 4 n^2+6 n+2-3 n^2-6 n-3 12 = n^2-1 12 aligned Given that Var (X) E(X) = 4 1 array ll & (n+1)(n-1) 12 (n+1) 2 = 4 1 & n-1 6 = 4 1 & n=1+24 & n=25 array