The accident probability at a new intersection is of interest to a traffic engineer. The engineer subjectively estimated the weekly accident probability as follows:

Weekly Accident Probability Subjective Probability of Accident Probability 0.1 0.30 0.2 0.40 0.4 0.20 0.6 0.05 0.8 0.04 0.9 0.01 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.