I have a question about how a result for the auto-correlation was calculated.
The autocorrelation function $R_X(t_1,t_2)$ is defined as $R_X(t_1,t_2) = E\left[X(t_1)X(t_2)\right]$
The stochastic process $X(t)$ is characterized by: $ X(t) = \begin{cases} +\sin t, \ \ p=1/4\\ -\sin t, \ \ p=1/4\\ +\cos t, \ \ p=1/4\\ -\cos t, \ \ p=1/4 \end{cases}$
The autocorrelation function result is: $R_X(t_1, t_2) = \frac12 \cos(t_2 - t_1)$. How was this reached? Specifically, I had trouble with applying the expectation over two different time instances.
Thanks, I appreciate any help.