5. Let X and Y be continuous random variables with joint density function $$f(x) = begin{cases} frac{1}{5}
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5. Let X and Y be continuous random variables with joint density function
$$f(x) =
\begin{cases}
\frac{1}{5} + cy & 0 < x < 1, 1 < y < 5 \\
0 & \text{otherwise}
\end{cases}$$
where c is a constant.
(a) What is the value of c?
(b) Are X and Y independent?
(c) Find P(X + Y > 3).
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