# CMPSCI 240: Reasoning About Uncertainty

### David Mix Barrington

### Spring, 2009

# Homework Assignment #2

#### Posted Wednesday 25 February 2009

#### Due on paper in class, Wednesday 11 March 2009

There are fourteen questions for 100 total points plus 10 extra
credit. All but the last one 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. The number in parentheses following each problem
is its individual point value.

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

- Problem 10.1.3 (10)
- Problem 10.1.6 (10)
- Problem 10.2.2 (5)
- Problem 10.2.4 (5)
- Problem 10.2.5 (10)
- Problem 10.3.1 (5)
- Problem 10.3.2 (10)
- Problem 10.3.5, part c only (5)
- Problem 10.5.2 (5)
- Problem 10.5.4 (5)
- Problem 10.5.5 (10 extra credit)
- Problem 10.6.2 (10)
- Problem 10.6.5 (10)
- Problem B-1 (10): Suppose I flip a coin and stop after the first
time I throw heads three times in a row. Let X be the total number of throws
I make. (For example, if the first three throws are all heads, X = 3.) What
is the expected value of X for a normal fair coin? What is the expected value
of X if the first throw is equally likely to be heads or tails, but every
subsequent throw has a 60% chance of being the same as the throw before it?

Last modified 25 February 2009