2. (10 points) Let X and Y have the joint pdf
\begin{equation*}
f(x,y) = \frac{3}{2}x^2(1-|y|), \quad -1 < x < 1, \quad -1 < y < 1.
\end{equation*}
• Find $P((x,y) \in A)$, $A = \{(x,y): 0 < x < 1, 0 < y < 1\}$
3. (10 points) Each of the 7 students in a class is given a fair 7-sided die. In addition, each student is
numbered from 1 to 7.
(a) If the students roll their dice, what is the probability that there is at least one \"match\" (e.g., student
4 rolls at 4)?
(b) If you are a member of this class, what is the probability that at least one of the other 6 students rolls
the same number as you do?
