Let X and Y be independent continuous random variables with respective hazard rate functions X(t) and Y(t), and set W = min(X,Y). (a) Determine the

Let X and Y be independent continuous random variables with respective hazard rate functions λX(t) and λY(t), and set W = min(X,Y).
(a) Determine the distribution function of W in terms of those of X and Y.
(b) Show that λW(t), the hazard rate function of W, is given by λW(t) = λX(t) + λY(t)