2. The random vector \( (x, y) \) has joint pdf given by \( f(x, y)=\left\{\begin{array}{ll}x+y & , 0 \leq x \leq 1 \text { and } 0 \leq y \leq 1 \\ 0 & , \text { elsewhere }\end{array}\right. \)
a.) Find the marginal density of \( X \).
b.) Find the marginal density of \( Y \).
c.) Find the conditional density of \( Y \) given \( X \).
d.) Find the conditional expectation and variance of \( Y \) given \( X \).
e.) Are \( X \) and \( Y \) Independent?