Question

Time headway in traffic non he elapsed tin e between the t ne hat one car finshes passing a fixed point and the nstant that he next car begins o pass that point. Let χ period af haavy flow. The pdf af X is the folowing. the tinie heed ay r two randomly chosen consecu ve cars on a free ay during a tx) - 0.16e-0.6 (a) what is the probability that time headway i at moat 5 sc? (Raund your anawer to three dacimal placas.) (b) what is the probability that time headway imcre than s ?At least s sec (Raund your answers to three deciml places.) mora than 5 sec at least S sec (C) What is the probability that time neadway is between 4 and 5 sec? 《Round your answer to three decimal places.)

Answer 1

a)P(X<5)=1-e^{-0.16*(5-0.5)} =0.513

b)

P(more then 5sec) =1-P(X<5)=1-0.513=0.487

P(at least 5 sec)=1-P(X<5)=1-0.513=0.487

c)

P(4<X<5)=0.084