Please answer Question 5. I attached the theorem below. Thanks!!

5. Using the method of proof for Theorem 2.8, can you find the pdf of X = max(X1, X2), where X1 ~ exp(1), X2 ~ exp(u), and X1, X2 are independent?Theorem 2.8: Let X1 ~ exp(l) and X2 ~ exp(,u) be independent and let X = min{X,,X,}. Then X ~ exp(1+p). This can, of course, be extended to more than two random variables. Then by Denition 3 of the last section, it follows that N1(t)+ N 2 (t) is a Poisson process at rate 1+ ,u. Now let's determine the probability that the next arrival is an emergency patient. This happens if and only if X1