I need solve part C

components and the way they are connected, the subsystem(s) and when - function, the entire system and when will it function) (5 points). C1 Cz Figure 2: A system with 3 components. Suppose that you consider an experiment that consists of determining the condition of each component (5 - success for a functioning component and F - failure for a nonfunctioning component). Suppose also that you define three events A, B and C as follows: A: exactly two out of the three components function, 3: at least two of the components function, C: the system functions. Describe and list the outcomes contained in the events A, B and C (5 points). Describe and list the outcomes contained in the following events: C", AUC, AnC, BUCandBnC(5points). [15 points] Consider the system shown in Figure 2. Let X1,X2 and X3 denote the lifetimes of components 1, 2, and 3, respectively. Suppose the XI '5 are independent of one another and each X; has the probability density function defined as /'l. f(x) = {39 x othercwigl where the parameter .1 > 0. Let 1' denote the system lifetime. Express the event (Y S y) in terms of unions and/or intersections of the three events (X1 S y), (X2 S y) and (X3 S y) (5 points). Obtain the cumulative distribution function of Y (10 points). Given that the expected value of a random variable is u = 1 compute the expected system lifetime (5 points). Calculate the probability 1' that the system lifetime exceeds a particular lifetime value to, assuming that the probability that any particular cell lasts more than to is 0.75. Explain in details all your calculations and assumptions (5 points). [25 points]