The average amount of time until a car accident on a particular 60 mile stretch of road is 30 minutes. Assume (unreasonably) that car accidents are independent, the time to a car accident is exponentially distributed, and that two accidents cannot occur at the same time. a. What is the probability of a car accident occurring in the first hour? b. What is the probability of a car accident occurring between 15 and 45 minutes? c. What is the variance of the time until a car accident occurs? If a car accident has not happened in 2 hours, what is the probability it will happen in the next hour?

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