Exercise 4 A system consists of 5 components. The times to failure for these components are independent exponential random variables with parameter A = 2. The system functions as long as at least 2 components are functioning. At time t = 0 all 5 components are functioning. Let T be the time to failure for the system. Find a) The probability density function of T b) 1P(T g 0.1) c) Var(T) Hint: In your answers, consider using the following theorem and lemma: Theorem 1 (Exponential order statistics and increments). Suppose that X1,...,Xn1' 39 d Exp()\\) and consider the order statistics of this random sample, i.e., X(1)0