Is the sum or product of two iid random process still a iid process? [closed]

Is the sum or product of two iid random process still a iid process? For example, let $X_n$ is iid Gaussian random process, and $U_n$ is iid binary random process, and they are independent to each other.

$Z_n=X_n U_n$;$Y_n=X_n +U_n$;$R_n=X_n + U_0$

Are $Z_n$,$Y_n$ and $R_n$ still iid processes?

closed as off-topic by Math1000, jvdhooft, Ethan Bolker, José Carlos Santos, The PhenotypeJun 12 '18 at 20:24

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Math1000, jvdhooft, Ethan Bolker, José Carlos Santos, The Phenotype
If this question can be reworded to fit the rules in the help center, please edit the question.

• For example $X,Y$ independent implies that $X+Y$ is independent: math.stackexchange.com/questions/1546247/… – Math1000 Jun 12 '18 at 10:11
• but they are variable,mine is process – XM551 Jun 12 '18 at 10:14
• Surely, yes. $Z_n,Y_n,R_N$ are all i.i.d.. – Kavi Rama Murthy Jun 12 '18 at 10:19
• can you give me some proof? – XM551 Jun 12 '18 at 10:21
• A stochastic process is a collection of random variables. In the case where they are indexed on the positive integers, it follows clearly from induction that if e.g. $X_1+U_1$ are independent then so too are $X_{n+1}+U_{n+1}$ for all $n$. – Math1000 Jun 12 '18 at 10:30