# Question

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)

(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)

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