Homework 9 (assigned August 17, due August 23)

1. Exercises 33, 35, 45, 48, 49, 59, 60, 62, and 81a, b, c, d on pages 238 and 239. (2 points each)

2. Exercises 3, 7, 18, 31, 32, 39, 40, 46, 47, and 53 on pages 249 and 250. (3 points each)

3. Exercises 2, 9, 12, 24, 26, 27, 29, 35, 36, and 39 on page 259 and 260. (3 points each)

4. Prove that if S is a sample space and A is an event, then S and A are independent events. Are two mutually exclusive events A and B (i.e., A and B disjoint) independent? (4 points)

5. Prove that if A and B are independent events, then so are the two pairs of events A and B', and A' and B', where A' and B' are the complements of the sets A and B respectively. (4 points)

6. Use mathematical induction to prove that 3 divides n³ + 2n whenever n is a nonnegative integer. (4 points)

7. Find an explicit formula for f (n) if f (1) = 1 and f (n) = f (n - 1) + 2n - 1 for n ≥ 2. Prove your result using mathematical induction. (4 points)

Gerry Brady
Wednesday August 17 11:53:44 CDT 2005