Question: 2018 Fall Final - 21

Author: Michiel Smid

You are given two independent random variables $X$ and $Y$, where

$\Pr(X = 0)$

$= \Pr(X = 1) = \Pr(Y = 0)$ $= \Pr(Y = 1) = 1/2.$

Define the random variable $$ Z = (X + Y)\ \mathrm{mod}\ 2. $$ Which of the following is correct?

(a)

All of the above.

(b)

The random variables $X$ and $Z$ are independent.

(c)

None of the above.

(d)

The random variables $X$ and $Z$ are not independent.