Given that the PMF is
\begin{array}{|c|c|c|c|} \hline x&-1 & 0 & 1\\ \hline f(x)&p & 1-2p & p\\ \hline \end{array}
and $E(2^X) = \frac{2}{3}$, find p.
Now, I clearly can't use $\sum f(x) = 1$ so I used $\sum 2^x f(x) = \frac{2}{3}$ yielding $2^{-1}p + 2^0(1-2p)+ 2^1p = \frac{2}{3}$ $\Rightarrow \frac{1}{2}p + 1-2p + 2p = \frac{2}{3}$
$\Rightarrow \frac{1}{2}p + 1 = \frac{2}{3}$
$\Rightarrow \frac{1}{2}p = \frac{-1}{3}$
$\Rightarrow p = \frac{-2}{3}$
But a negative answer doesn't make sense.