Chapter 8 Day 2

Warm - Up A believer in the “random walk” theory of stock markets thinks that an index of stock prices has probability of 0.65 of increasing in any year. Moreover, the change in the index in any given year is not influenced by whether it rose or fell in earlier years. Let X be the number of years among the next 6 years in which the index rises. X has a binomial distribution. What are n and p? What are the possible values that X can take? What is the probability that the index rises 4 years? What is the probability that the index rises at least 4 years?

Homework Solutions 1. A) no B) no C) yes 2. A) yes B) no C) no 3. A) .2637 B) use calculator 4. A) Symmetric B) use calculator C) .0078 5. A) .9437 B) 3/5 6. A) .1032 B) .1576 C) .8424

Simulations Back to the pizza problem… Jack burns 15% of all pizzas. He cooks 9 pizzas. Construct a simulation to estimate the probability of burning three pizzas or fewer. Describe the design of your experiment, including the correspondence between digits and outcomes in the experiment. Take 25 samples. How does this compare to the theoretical probability?

Mean and Standard Deviation of a Binomial Random Variable If a count X has the binomial distribution with number of observations n and probability of success p, the mean and standard deviation of X are

Example Jack burns 15% of his pizzas. If he cooks 9 pizzas, how many will he burn on average? What is the standard deviation of the number of pizzas burned? What is the probability of exactly 7 pizzas cooked (not burned)? What is the probability that at least 1 of the pizzas is burned?