# Homework Assignment #2

#### 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.

• 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?