17.5. Linearity of Expectation 611
- The single 20 point question is awarded either 12 or 18 points with
equal probability.
Lecturersscore an exam by rolling a fair die twice, multiplying the results,
and then adding a “general impression”score.- With probability 104 , the general impression score is 40.
- With probability 103 , the general impression score is 50.
- With probability 103 , the general impression score is 60.
Assume all random choices during the grading process are independent.
(a)What is the expected score on an exam graded by a TA?(b)What is the expected score on an exam graded by a lecturer?(c)What is the expected score on a Math for Computer Science final exam?Class Problems
Problem 17.10.
Let’s see what it takes to make Carnival Dice fair. Here’s the game with payoff
parameterk: make three independent rolls of a fair die. If you roll a six
no times, then you lose 1 dollar. exactly once, then you win 1 dollar. exactly twice, then you win two dollars. all three times, then you winkdollars.For what value ofkis this game fair?Problem 17.11.
A classroom has sixteen desks in a 4 4 arrangement as shown below.