Question: Redo Problem II assuming the weekly rate has a prior distribution that is exponential with a mean of 0.2 per week.
Problem II: In Problem I, assume that a weekly rate is used with a uniform prior distribution over the range 0.1 to 0.5 per week. Use an exponential likelihood function. Determine the posterior distribution based on additional information that an accident occurred in less than 2 weeks.
Problem I: The accident probability at a new intersection is of interest to a traffic engineer. The engineer subjectively estimated the weekly accident probability as follows:
Solve the following:
a. What is the average accident probability based on the prior information?
b. Given an accident in the first week of traffic, update the distribution of the accident probability.
c. What is the new average accident probability based on the posterior information?
d. Given an accident in the first and second weeks and no accidents in the third week of traffic, update the distribution of the accident probability.
e. What is the average accident probability after the second week?
f. Given no additional accidents for the weeks 4, 5, 6, 7, 8, 9, and 10, update the distribution and the average accident probability. Plot your results. Discuss the results.