If I have a process Xn that is made of two sequences of independent random variables. For n being even , Xn is either +1 or -1 with probability 1/2 , but for n odd , Xn is either 1/5 or -5 with probabilities 25/26 and 1/26 respectively.
How could I prove Xn is a strict stationary process without proving it is wss(wide-sense stationary) first?.
I have tried dividing it into two random variables say X1n and X2n and calculating the mean value of them E[X1n]=0 and E[X2n]=0 , but I can't take it further. Can anyone help?
A strictly stationary $\left(Y_n\right)_{n\in\mathbb Z}$ sequence have the particularity to be identically distributed, that is, for all $n$, $Y_n$ has the same distribution as $Y_0$.
Here, $X_1$ does not have the same distribution as $X_2$.