[tex]P((x-E(x))^2)\: =\: P(x^2)[/tex]
[tex]P(x^2=0)\: =\: P(x=0)\: =0[/tex]
[tex]P(x^2=1)\: =\: P(x=1)\: +\: P(x=-1)\: =\frac{1}{6}+\frac{1}{6}=\frac{2}{6}[/tex]
[tex]P(x^2=4)\: =\: P(x=2)+P(x=-2)\: =\frac{2}{6}+\frac{2}{6}\: =\: \frac{4}{6}[/tex]