According to an estimate, the Pan Island Expressway (PIE) has an average accident of 441 per year (365 days) in 2013. Assume the daily rate of accidents follows Poisson distribution and the average yearly accident rate stays constant throughout the years.
(a) Find the probability of having no accident for at least 3 consecutive days.
(b) Find the average number of consecutive days without accidents.
(c) Find the standard deviation for number of consecutive days without accidents.
(d) Why is it that the authorities’ efforts in reducing yearly accident rate on PIE also tend to increase the variability of interval between accidents?
