5. Assume that customers arrive as a Poisson random process with parameter X. Let T, and T, be the arrival time of the first customer and the second customer. Also, Let W. and W, be the first two inter-arrival time. (a) Find the joint pdf fw, w(W1, wa). (b) Find the joint pdf frtoti,ta). (Hint: First identify the mapping from (W1,W2) to (T:,12) and then use the results you obtain from part (a).) (c) Compute the marginal pdf fr,(t2) and verify that it agrees with the answer we got in class. (a) What is the probability of event A, that there was exactly one arrival in the period (0,r)? (e) Find the conditional joint pdf fin,12A(61, 62|A). Hint: A is equivalent to the event that {T,