I'm looking at an example from a book I'm reading,
How does it formulate the mean? I am thinking $$E[X[n]] = \sum\limits^\infty_{-\infty} X[n]P[X[n]] =\\ \sum\limits^\infty_{n=-\infty} X[n = even] \frac{1}{2} + X[n = even] \frac{1}{2} + X[n = odd] \frac{9}{10} + X[n = odd] \frac{1}{10} \\ = \sum\limits^\infty_{-\infty} \frac{1}{2}-\frac{1}{2}+\frac{1}{3}\frac{9}{10}-3\frac{1}{10} = 0$$ Does this formulation look right? I'm confused when X[n] can be probabilistically assigned values.