a. Choosing any two intervals you have judged to have equal probability content, and — Choose course that are currently taking which the final exam worth 100

Choose a course that you are currently taking in which the final exam is worth 100 points. Treating your score on the exam as if it were a continuous uncertain quantity, assess the subjective probability distribution for your score. After you have finished, check your assessed distribution for consistency by:

a. Choosing any two intervals you have judged to have equal probability content, and

b. Determining whether you would be willing to place small even-odds bets that your score would fall in one of the two intervals.(The bet would be called off if the score fell elsewhere.)

c. After assessing the continuous distribution, construct a three-point approximation to this distribution with the extended Pearson-Tukey method. Use the approximation to estimate your expected exam score.

d. Now construct an approximation using the extended Swanson-Me gill method. Use this approximation to estimate your expected exam score. How does your answer compare with the estimate from part c?

SOLUTION

This question requires students to make personal judgments. As an example, suppose the following assessments are made:

P (S ≤ 65) = 0.05

P (S > 99) = 0.05

P (S ≤ 78) = 0.25