I am unable to solve this homework question and was hoping to get some help for part (a).
I know that $Z$ is a stationary process because its generating function does not change with time. By the opposite reasoning, $W$ is not stationary because the coin flip happens at every time $n$.
For the second part of (a), I had thought that $Z$ would be IID because the probability of the events are independent and occur with the same distribution. $W$ is not IID because of the coin flip occurring at every time $n$ which means its distribution at time $n$ is different than all other times.
The answer turned out to be the opposite but I don't understand why.
PS: Don't worry its not an actual homework https://documents.epfl.ch/groups/i/ip/ipg/www/2015-2016/Information%20Theory%20and%20Coding/hw5.pdf