9. A uniform small cube has six faces, three of which are marked with the number 0, two with the number 1, and one with the number 2. If this small cube is tossed twice, then the mathematical expectation of the product of the numbers facing up is



Translating the text into English while preserving the original format and line breaks, the result is as follows:
Let the product of the upward numbers be $X$, then $X=0,1,2,4$. And $P(X=0)=\frac{1}{2}+\frac{1}{2} \cdot \frac{1}{2}=\frac{3}{4}, P(X=1)=\left(\frac{1}{3}\right)^{2}=\frac{1}{9}$, $P(X=2)=2 \cdot \frac{1}{3} \cdot \frac{1}{6}=\frac{1}{9}, P(X=4)=\left(\frac{1}{6}\right)^{2}=\frac{1}{36}$. Therefore, $E X=1 \cdot \frac{1}{9}+2 \cdot \frac{1}{9}+4 \cdot \frac{1}{36}=\frac{4}{9}$.