CMPSCI 291b: Reasoning About Uncertainty

David Mix Barrington

Spring, 2008

Homework Assignment #2

Posted Thursday 28 February 2008

Due on paper in class, Wednesday 12 March 2008

There are twelve questions for 100 total points. credit. All but the last two are from the textbook, Mathematical Foundation for Computer Science. Note that the book has both Exercises and Problems -- make sure you are doing a Problem and not the Exercise with the same number. Numbers in parentheses following each problem are its individual point value.

Students are responsible for understanding and following the academic honesty policies indicated on this page.

• Problem P.1.1 (5)

• Problem P.1.2 (5)

• Problem P.1.4, all parts (10)

• Problem P.1.5 (10)

• Problem P.2.2 (5)

• Problem P.2.4 (10)

• Problem P.2.5 part a only (10)

• Problem P.3.1 (5)

• Problem P.3.3 (10)

• Problem P.4.1 (10)

• Problem X1 (10) In a hand of Texas Hold'em, the five cards on the table consist of two aces, a two, a three, and a four.
  • (a) What is the probability that a given player is holding one or more of the two remaining aces?
  • (b) Under the (incorrect) assumption that each player's chance of having an ace is independent, what is the probability that at least one of four players has one or more aces?
  • (c) If there are four players, what is the actual exact probability that at least one of them has at least one ace?

• Problem X2 (10) Over the probability space for poker dice (five six-sided dice rolled independently) let f be the random variable that is the sum of the numbers on the six dice and let g be the random variable that is the number of sixes thrown. Compute the mean and variance of both f and g.

Last modified 28 February 2008