Proof of strictly stationary process

[trenekas]

Hi all. I need to prove or disprove if process $Y_n=1/2*X_n+1/4*X_{n-1}+1/8*X_{n-2}$ are stricly stationary. $X_n,n\in R$ i.i.d.
So almost i have the answer. But don't know if it is correct or not. I have a question of situation when $\Gamma_Y(t,s)$ and |t-s|≤2 for example:
$Y_{10}=1/2*X_{10}+1/4*X_{9}+1/8*X_{8}$
$Y_8=1/2*X_8+1/4*X_{7}+1/8*X_{6}$
There are $x_8$ in both but situations and not sure if $Y_{10}$ and $Y_{8}$ are i.d.
Hope you understand my problem.
Maybe its a little stupid question but I'm just started to learn random processes. :)
Thanks for help.

 

[mathman]

The Y's will be correlated as you noticed. The correlation depends only on the parameter difference.
However, the distributions will be identical, since the X's have identical distributions.

Put these together and you get strictly stationary.