TIFR ECE 2013 | Question: 14

Question

$X, Y, Z$ are integer valued random variables with the following two properties:

1. $X$ and $Y$ are independent.
2. For all integer $x$, conditioned on the event $\{X=x\}$, we have that $Y$ and $Z$ are independent (in other words, conditioned on $X$, the random variables $Y$ and $Z$ are independent).

Which of the following can we infer?

• A. The random variables $X$ and $Z$ are independent
• B. Conditioned on $Y$, the random variables $X$ and $Z$ are independent
• C. Conditioned on $Z$, the random variables $X$ and $Y$ are independent
• D. All of the above
• E. None of the above