Q3: Assuming the time intervals between any.' two consecutive 11M minibuses are independent and is uniformly distributed in [0, t] for some L50. We want to estimate I from n samples of the arrival time intervals between consecutive minibuses: t1, t2, , it". (i) [IOpt] Find an unbiased estimator of t (you need to prove it is unbiased). (ii) [lOpt] Find the maximum likelihood estimator 5mg oft. (Hint: You do not need to take derivatives for this maximization). {iii} [Spt] ls Ems in (ii) unbiased? Prove your result by calculating its bias. (Hint: First, nd the cdf of' Em]:- and note that \"maxf. Y) S a\" is always equivalent to \"X 5 a and Y S a"). (iv) [IOpt] Suppose we know t=10 min. One minibus has just left. and there are still 40 people in front ofyou in the queue for the minibus. Assuming each arrival minibus has 16 seats available. how long are you expected to wait until you get on an 1 1M