Mathematics for Computer Science

(Frankie) #1

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.

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