A random variable X assumes value 1,2,3, . n with equal probabilities. If the ratio of variance of = p_i x_i^2- ( p_i x_i )^2 to expected value of X is equal to 4 , then the value of n is

Step-by-step solution

aligned & Variance = p_i X_i^2- ( p_i X_i )^2 & = 1 n n(n+1)(2 n+1) 6 - 1 n n(n+1) 2 ^2 & = n(n+1) 2 n 2 n+1 3 - n(n+1) 2 n & Expected value = p_i x_i= 1 n n(n+1) 2 = n(n+1) 2 n & Ratio = 2 n+1 3 - n(n+1) 2 n aligned n^2-25 n=0 n(n-25)=0 n=0 or n=25 n=25 as n=0 is not possible