If X is the number of points rolled with a balanced die find

If X is the number of points rolled with a balanced die, find the expected value of u(X)=2X².

Solution

the expected value of points rolled with a balanced die is E(X) = 1*1/6+2*1/6+3*1/6+4*1/6+5*1/6+6*1/6 = 21/6 = 7/2 =3.5 Clearly mention what is U(X) if U(X) = 2X2 then E(U(X)) = E(2X2) = 2E(X2)= 2E(X)*E(X) = 2*(7/2)*(7/2) = 49/2