$E[X_i^2]$ if I already know $E[X_i]$.

Question

I have calculated $E[X_i] = \frac{2}{3}$ and therefore I know that $E[X_1] = \frac{2}{3}$. Now I want to calculate $E[X_1^2]$. Is it correct to calculate with the following process?

$E[X_1^2] = E[X_1 \cdot X_1] = E[X_1] \cdot E[X_1] = \frac{2}{3} \cdot \frac{2}{3} = \frac{4}{9}$

X1 can either be 1 or 0.

No variance is included in the problem I have to solve.

Edit: The above formula is incorrect. The correct one is the one at the accepted answer.

Answer 1

Since $X_i$ is either $1$ or $0$ it follows that $$ 2/3=E(X_1)=P(X_1=1). $$ Hence $$ E(X_1^2)=1^2P(X_1=1)+0^2P(X_1=0)=2/3. $$