1. (a) Let X and Y be independent and non-negative, and identically distributed with density f(x) and distribution F(x). Let U = min{X, Y) and V = max{X, Y}. Find the condi- tional density of U given V, and find E(U|V = v). (b) A satellite has two transmitters; their lifetimes are independent and exponential with parameter 2. The satellite operates if they both work. Transmissions cease at time . Show that the expected failure time of the first to fail is atipli (It was launched at time 0.) 1 1 Tee 1. (a) Let X and Y be independent and non-negative, and identically distributed with density f(x) and distribution F(x). Let U = min{X, Y) and V = max{X, Y}. Find the condi- tional density of U given V, and find E(U|V = v). (b) A satellite has two transmitters; their lifetimes are independent and exponential with parameter 2. The satellite operates if they both work. Transmissions cease at time . Show that the expected failure time of the first to fail is atipli (It was launched at time 0.) 1 1 Tee