I have to work out whether its weakly stationary or not
Xt = b where b is a constant.
I know i have to work out that the mean first and make it finite and not dependent on t.
What does E[ ] = ????
Do you by any chance mean
= b + where e is a zero mean independent identically distributed noise process with a variance?
If so = + a bunch of mean zero terms with variance equal to var(e)/(1-b^2). Since b^n converges to zero the series is stationary.
As you have it written is generated by repeated draws from an iid distribution and isnt really a time series.