Decision-analysis for management

1. Use the probability wheel and direct estimate methods to elicit a colleague"s subjective probabilities for the outcomes of a forthcoming sports event (e.g. a snooker tournament). Check for consistency between the assessment methods and use the addition rule to evaluate the coherence of the probabilities that your colleague has assessed.

2. Use the probability method to elicit a colleague's subjective probability distribution for his or her marks in their next decision-analysis assignment.

3. Repeat the above exercise for predictions of the starting salary distribution in his or her first employment after completing their current educational course of study.

4. An electricity company supplies power to consumers in the Eastern region of a country. When the demand for power exceeds the capacity of the cheapest generating station a second station is brought 'on-line.' One of the company's managers makes a daily judgment about the probability that the second station will be required at least once in the following day. The records of his judgments are given below for a period of 600 days.

Probability assessed by manager0 0.2 0.50.81.0

Number of days this probability judgment was made 40160180120 100

Number of days the second station was used 850110110100

(a) Plot a calibration curve for the manager and interpret the result.

(b) Calculate the manager's average Brier score.

(c) Suppose that the manager had simply quoted a probability of 0.5 on all 600 days, what would his Briar score have been?