(Solved): Suppose \( X \) and \( Y \) are random variables with the given joint density function. \[ f(x, y) ...

Suppose \( X \) and \( Y \) are random variables with the given joint density function. \[ f(x, y)=\left\{\begin{array}{ll} 0.1 e^{-(0.5 x+0.2 y)} & \text { if } x \geq 0, y \geq 0 \\ 0 & \text { otherwise } \end{array}\right. \] (a) Is \( f \) a joint density function? \begin{tabular}{|l|} \hline Yes \\ No \\ \hline \end{tabular} (b) Find \( P(Y \geq 6) \). (Round your answer to four decimal places.) Find \( P(X \leq 8, Y \leq 3) \). (Round your answer to four decimal places.) (c) Find the expected value of \( X \). Find the expected value of \( Y \).