## Homework 4

#### Due Wed. Sept. 29 at 11:59pm

Homework policies and submission instructions

## 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) A student invests on three risky projects. He will spend $100 on each project. Let S1, S2 and S3 be the events that the first, second and third project respectively return some money. Suppose all events are mutually independent and $$p_1 = P(S1)=0.2$$ and $$S1$$ returns$1000, $$p_2 = P(S2)=0.3$$ and $$S2$$ returns $500, $$p_3 = P(S3)=0.6$$ and $$S3$$ returns$200. Let $$W$$ be the random variable that represents the student's net returns in dollars.
1. Calculate the possible values for $$W$$ and the corresponding probabilities
2. What is the expected value of the winnings, $$E[W]$$ ?
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.