9. [15 points] A room is lit by two light bulbs which are connected in a series Circuit. If either light bulb fails, the room will go dark. Let A and B denote the lifetimes (in years) of these two light bulbs. Assume that A N Exp(2), that B N Exp(3), and that A and B are independent of each other.1 (a) Let C denote the time when the room goes dark. Find the pdf of C. (b) What is E[C]? Hint: the pdf you obtain in part (a) should be of a familiar type. (c) Suppose light bulb B burns out rst. You then move light bulb A to another room, where it is the only bulb. Starting at the time it is turned on in the new room, what is the expected lifetime of bulb A in the new room? Hint: this question can be answered independently of parts (a) and (b)