申論題

5. You are waiting for a taxi. The inter-arrival time interval between two taxi arrivals is random, say T, and inter-arrival time intervals are independent. You know that T has an exponential distribution and that the probability density function of T is parameterized by μ ＞ 0 as follows: 

 (a) You know that the previous taxi arrival is s time ago. Let TR be the remaining time you have to wait for the next taxi arrival. Derive the probability that you will need to wait for no more than a time duration r, knowing that the previous arrival was s time ago. (You need to give the derivation, not just the answer. 10%)