(5) 5. A system consists of three components connected a) in series ; b) in parallel. Suppose that i-th component has a lifetime that is exponentially distributed with A; = .01, A2 = .02 and A3 = .05, and that components fail independently. Let X = the time at which the system fails. a) Calculate the cdf F(a:) = P(X S 3:), the pdf of X and the expected value of X for both cases. b) Determine the probability that the system will not fail before 300 hours for both cases. Him: use notation X. = lifetime of i-th component, A.- = {X- 2 x},A = {X 2 x},t = 1, 2, 3; use the fact that EX = 1/)\\ forX ~ Exp\")