Hw_7_Highway_safety - CEE 597 Risk Analysis and Management...

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C E E 5 9 7 – R i s k A n a l y s i s a n d M a n a g e m e n t Homework Assignment #7 Readings for Highway Safety National Research Council (NRC), "55: A Decade of Experience," Exec. Summary & Appendix material (Packet) [NRC presents a statistical analysis of a complex & significant problem. ] Read Lave (one page; packet), "Costs of Going 55" for Wednesday, 3/12/2008 Homework Due Wednesday, March 26, 2008 (after spring break) 1. Parameter estimation for a Poisson process: (a) If, on average, airline accidents occur at a rate of 0.152 accidents per million flights (i.e. 5/33 million flights), what is the probability of exactly 5 accidents between 1979 and 1986, as reported in the table in last week’s homework? [Here passage of time is measured not in minutes but in flights.] [ 0.15 < p < 0.2 ] (b) If I started waiting today for another 3 accidents to occur so that I would have more data for my test, what are the mean and standard dev. of the length of time (in yrs) that I would have to wait (assuming the accident rate didn't change)? [μ 5 yrs; σ 3 yrs] (c) If I estimate the arrival rate λ of accidents from 5 accidents in 33 million flights, what is the estimate of λ , and the variance and standard error of that estimator?
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