Question

Question C

C. Suppose that during each minute there is a 1 in 500, 000 probability that there is an accident at a particular intersection (independently of all other minutes). Using the approximation of 500,000 minutes per year, we expect to see 1 accident per year on average. One year somebody proposes to install a new kind of stoplight to reduce accidents. You believe a priori that there is a 1/5 chance that the new stoplight is effective, in which case it will reduce the accident rate by fifty percent, and a 4/5 chance it will have no effect. The new stoplight is installed and during the next 18 months there are no accidents. Using Poisson approximations, compute your updated estimate of the probability that the light is effective. Remark: It is often hard to tell whether preventative measures against rare events are having an effect. With twenty years of data we might be more confident, but by that point accident rates may have changed for other reasons (e.g., self driving cars). On the other hand the k! in the Poisson denominator means that large numbers are ertremely unlikely. If we suddenly see 10 accidents in one year, we should seriously question our assumption that the number is Poisson with

Answer 1

Minutes 2 500,000 o,000 0 50u,000 00000 O.1S zera acc dents bey Poissan's distehuhan 0.223 0.529