Solution: 2018 Fall Final - 21
Author: Michiel SmidQuestion
You are given two independent random variables $X$ and $Y$, where
Define the random variable
$$
Z = (X + Y)\ \mathrm{mod}\ 2.
$$
Which of the following is correct?
| $\Pr(X = 0)$ | $= \Pr(X = 1) = \Pr(Y = 0)$ $= \Pr(Y = 1) = 1/2.$ |
(a)
None of the above.
(b)
The random variables $X$ and $Z$ are not independent.
(c)
The random variables $X$ and $Z$ are independent.
(d)
All of the above.
Solution
Linearity of Expectations allows this to exist without crushing it; therefore, independent