Suppose $X$ is equally likely to take three values: $−1, 0, +1$.
Let $Y = X^2$.The probability mass function for random variable Y is $P(Y=0)=\frac 13$ and $P(Y=1)=\frac 23$
Here is the thing, when I calculate the variance of Y
$$var(Y)=E(Y^2)-(E(Y))^2$$
Using the given equation, the result I got was $E(Y)=E(Y^2)$. That makes the $var(Y)<0$ which is wrong. Could someone show me what's wrong with my calculation? Thanks in advance.