1. A machine is subject to two independent causes of failure. The time of the first cause of failure is uniformly distributed on the interval [0, 4]. The time of the second cause of failure is uniformly distributed on the interval [0, 5]. Find the probability that: (a) the machine will fail from cause 1 before time 3; (b) the machine will eventually fail from cause 2.
2. Two failure times T1 and T2 have a joint distribution given by the joint density function
Find: (a) FT,J (t, 1) and FT,J (t, 2); (b) the distribution of J; (c) μ(t, 1) and μ(t, 2).