Question: Read Problem II assuming the annual rate has a prior distribution that is exponential with a mean of 15 per year.
Problem II: In Problem I, assume that an annual rate is used with a prior uniform distribution over the range 10 to 18 per year. Use an exponential likelihood function. Determine the posterior distribution based on additional information that an injury occurred in less than 2 weeks (i.e., 0.04 year).
Problem I: The probability of back injuries of construction workers at XYZ Corporation is of interest to a safety engineer. The engineer subjectively estimated the annual probability as follows:
Solve the following:
a. What is the average annual probability based on the prior information?
b. Given no back injuries in a year, update the distribution of the annual probability.
c. What is the new average annual probability based on the posterior information?
d. Given injuries in the first and second years and no injuries in the following year, update the distribution of the annual probability.
e. What is the average annual probability after the second year?
f. Given no additional injuries for the years 4, 5, 6, 7, 8, 9, and 10, update the distribution and the average annual probability. Plot your results, and discuss the results.