Question: Let X and Y be indpendent exponential random variables with parameters ? and ? , respectively. Define Z = min{X, Y}. a) Show that Z

Let X and Y be indpendent exponential random variables with parameters ? and ?, respectively. Define Z = min{X, Y}.

a) Show that Z is independent of the event{X

b) FindP(X = Z).

c) Define U = max{X ? Y, 0} =: (X ? Y)+. Find the distribution of U.

d) Define V = max{X, Y} ? min{X, Y}. Find the distribution of V.

6-6 (20) Let X and Y be indpendent exponential random variables with parameters 11 and ,u, respectively. Define Z = min {X , Y}. a) Show that Z is independent of the event {X

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