The p.m.f. of a random variable X is P (x)= array cl 2 x n ( n +1) & , x=1,2,3, n 0 & , otherwise array . , then E ( X ) is

Step-by-step solution

array |l|c|c|c|c|c| & 1 & 2 & 3 & & n (X) & 2 n(n+1) & 4 n(n+1) & 6 n(n+1) & & 2 n n(n+1) array aligned E ( X ) & = x_ i P (x_ i ) & =1 2 n ( n +1) +2 4 n ( n +1) +3 6 n ( n +1) & + + n 2 n n ( n +1) & = 2 n ( n +1) (1+4+9+ + n ^2 ) & = 2 n ( n +1) (1^2+2^2+3^2+ + n ^2 ) & = 2 n ( n +1) n ( n +1)(2 n +1) 6 & = 2 n +1 3 aligned