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: 

(b) Now (time 0), you decide not to take a taxi but to count the number of taxi arrivals in a period [0, τ]. Let the number of arrivals in [0, τ] be K, which is a RV. Derive Prob(K = 0). (You need to give the derivation, not just the answer. 5%)