Let $V_1$,$V_2$, $r$ be independent random variables, where $V_1$, $V_2$ are Gausian with the same distribution and $r$ is uniformly distributed in $[0,1]$ if
$X(t)=V_2 I(r \geqslant t)+V_1 I(r
a)find the mean of this process:
For the expectation I have the following:
$\mathbb{E}X(t)=μ(1-t)+μ t=μ$
b) find the autocorrelation function of this process
$R(t,s)=\mathbb{E}( X(t) X(s) )$
I have simplified this as much as I can, I don't know why I can't copy and paste what I have done, when I try only some of it appears. I have simplified it down to $\sigma^2$ * probability of union of the indicator functions and a similar expression with the mean.