The proportions X and Y of two chemicals found in samples in an insecticide have the
joint probability density function
$$
f(x,y) = \begin{cases}
2 & \text{if } 0 \le x \le 1, 0 \le y \le 1, 0 \le x + y \le 1, \\
0 & \text{otherwise}.
\end{cases}
$$
(a) Provide the marginal probability density function of Y at 0.7, i.e., provide $f_Y(0.7)$.
(b) Provide the conditional probability density function of X given Y = 0.7.
(c) Provide $P(X > 0.95 | Y = 0.7)$.
(d) Provide $E(X)$.
(e) Provide $E(X + Y)$.
(f) Provide $V(X + Y)$.
