Let Y(t) be a Random Process with mean $E[Yi]=0$. Find the mean value of $X(t) = Y(1) + Y(2) + ...+ Y(t)$ and then find autocorrelation X(t) Rx(n, m)

Question

$E[X(t)]$=

$E[Y1+Y2+⋯+Yt]$ =

$E[Y1]+E[Y2]+⋯+E[Yt]$ = 0.

Then I got stuck trying to find Rx(n, m) of X(t) process. I'm still learning random processes, am I right in saying it's a wide-sense stationary process due to E[X(t)] = 0? Then,

$Rx(n,m) = (Cov(X(n),X(m)) = E[X(n)X(m)]$ =

$E[X(n)(X(n) + Yn+1 +Yn+2 +⋯ + Ym)]$ =

$E[X(n)^2] + E[X(n)]E[Yn+1 + Yn+2 + ⋯ + Ym]$ =

$E[X(n)^2]$.

Is this correct? If not, where did it go wrong?