### Homework #2

#### Due: Feb 24th, 2014

1. Text Exercise 2.13(a)

2. Text Exercise 2.20

3. Text Exercise 2.21

4. Text Exercise 2.24

5. We said in class that the expected number of trials until a collision is found when throwing balls into $N$ bins is $\sqrt{\pi N/2}$. I want to know what the expectation is until the second collision. Do this empirically: write a program that throws balls into 1000 bins at random and records the number of throws when the first collision occurs, and the second. Do this 1000 times and give the averages. The first collision should agree with the formula above. What is the constant $c$ you get for the second collision where the expectation is $c\sqrt{N}$?