Let X 1 ,...,X n be i.i.d. random variable from the negative exponential distribution for which the density is (1.5.49), and let   Show that XXXXXXXXXXholds with T = 0 and   A system has two...

Let X₁,...,X_n
be i.i.d. random variable from the negative exponential distribution for which the density is (1.5.49), and let
  Show that (6.2.41) holds with T = 0 and

A system has two components connected in series, so that it fails when at least one of the components fail. Suppose that each component has a negative exponential life distribution [define by (1.5.59)] with mean θ. What is the life distribution of the system? Suppose that there are n copies of this system, and let their lifetimes be denoted by Y₁,...,Y_n, respectively. Show that