Question: 2022 Winter Final - 22
Let $D_1$ and $D_2$ be the result of tossing a $6$-sided die twice. Define the random variables
\[ X=2\cdot D_1 \]
and
\[ Y=
\begin{cases}
1 & \text{if $D_1+D_2=7$} \\
0 & \text{otherwise.} \enspace .
\end{cases}
\]
Which of the following is true?
(a)
None of the above
(b)
$X$ and $Y$ are independent
(c)
$X$ and $Y$ are not independent