If three random variables have the joint density [f(x, y, z)=left{begin{array}{lc}k(x+y) e^{-z} & text { for } 0 Y) and (Z>1).

If three random variables have the joint density

\[f(x, y, z)=\left\{\begin{array}{lc}k(x+y) e^{-z} & \text { for } 00 \\0 & \text { elsewhere }\end{array}\right.\]

find

(a) the value of \(k\);

(b) the probability that \(X>Y\) and \(Z>1\).