Two Components of a Minicomputer Have the Following Joint Pdf $f ( x , y ) = \left\{ \begin{array} { l l } x e ^ { - x ( 1 + y ) } & x \geq 0 \text { and } y \geq 0 \\0 & \text { otherwise }\end{array} \right.$

Essay

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y: $f ( x , y ) = \left\{ \begin{array} { l l } x e ^ { - x ( 1 + y ) } & x \geq 0 \text { and } y \geq 0 \\0 & \text { otherwise }\end{array} \right.$
a. What is the probability that the lifetime X of the first component exceeds 3?
b. What are the marginal pdf"s of X and Y? Are the two lifetimes independent? Explain.
c. What is the probability that the lifetime of at least one component exceeds 3?