Problems

1. (10 points) Textbook problem 4.2
2. (10 points) Textbook problem 4.6. Express your answers using choose and/or summation notation. There's no need to compute numerical answers.
3. (10 points) Textbook problem 4.7
4. (10 points) Textbook problem 4.20. You must state the method for dividing the stakes and calculate how much should be given to each player.
5. (10 points) Textbook problem 4.23. Do both parts of this problem. For part (b) of this problem, simulate with \( N = 10^5 \) trials and submit your answer as a graph (plot) of a function of \( p \) where \( p = 0.1, 0.2, \ldots, 0.9, 1 \). Submit your code for this problem by pasting it in your pdf, not in a separate file.
6. (2 extra points) Textbook problem 4.14.