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 it is or it is not wide sense-stationary?
side question : I know that the distribution is different , but if the probabilities where the same , would the distributions be considered the same? (meaning: +1 or -1 with probability 1/2 for even numbers , and 1/5 or -5 with probability 1/2 for odd numbers ) or to say the distributions are the same it should be : +1 or -1 with probability 1/2 for even numbers, and 1 or -1 with probability 1/2 for odd numbers)