Problems

1. (5 points) Textbook problem 4.3
2. (10 points) Textbook problem 4.5. In parts (a) to (d), your answers should be probability distributions. In part (e), provide an explanation for your answer.
3. (5 points) Textbook problem 4.7
4. (5 points) Textbook problem 4.11. Assume the players are drawing from a standard deck without replacement.
5. (5 points) Textbook problem 4.14
6. (5 points) Textbook problem 4.17
7. (5 points) Textbook problem 4.20. You must state the method for dividing the stakes and calculate how much should be given to each player. Textbook problem 4.21 provides a hint.
8. (10 points) Textbook problem 4.23. Do both parts of this problem by simulation with \( N = 10^5 \) trials and submit your answers as graphs of functions of \( p \) where \( p = 0.1, 0.2, \ldots, 0.9, 1 \). Submit your code for both parts of this problem by pasting it in your pdf, not in separate files.