Question: 2017 Winter Final - 21
You are given a fair red die and a fair blue die. You roll each die once, independently of each other.
Let $(i,j)$ be the outcome, where $i$ is the result of the red die and $j$ is the result of the blue die.
Define the random variables
$$
X = |i - j|
$$
and
$$
Y = \max(i, j).
$$
Which of the following is true?
(a)
The random variables $X$ and $Y$ are not independent.
(b)
The random variables $X$ and $Y$ are independent.
(c)
None of the above.