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?