A random variable X takes only 3 values {0, 1, 2} with $P(X=0)=P(X=1).$ If $E(X^2)=1+E(X)$ then the var(X) is :

$\frac{3}{4}$ 1 $\frac{11}{16}$ $\frac{9}{16}$

$\frac{11}{16}$