2019 October 14,

Math 265: Day 13

Carleton College, Joshua R. Davis

The first three problems come from our Poisson tutorial. I expect you to solve the other tutorial exercises but not hand them in. If you get stuck, then read your textbook. Many of them are worked out there.

A. Poisson tutorial Exercise 5 (earthquakes).

B. Poisson tutorial Exercise 6 (radioactive decay).

C. Poisson tutorial Exercise 7 (leukemia).

The other problems assigned today are also related to the Poisson distribution.

D. Section 4.12 Exercise 27. (In part b, don't let the word "moment" confuse you. Just compute E(X3).)

E. An entrepreneur is considering whether to build a motel in a certain location near a highway. Her research suggests that an average of 35 car-loads of people seek accommodation near that location each day. She assumes that each car-load will occupy one room for one night. How many rooms should the motel have, so that it is full 95% of the nights?

Each stream in the USA has an established baseline elevation. When the stream floods, its elevation increases by some number of feet. A 100-year flood is a flood of such severity that it is expected to occur once every 100 years. For example, a certain part of the Cannon River has a 100-year-flood level of 3 feet, meaning that it floods 3 feet once (on average) every 100 years. In any given stream and any given 100-year period, the number of 100-year-floods is well modeled as a Poisson random variable X.

F. What is λ such that X ~ Pois(λ)? How shocked are you when three 100-year-floods happen in a single 100-year period — meaning, what is the probability of that happening?

G. Sometimes 100-year-floods are described in this way: "Each year, there is a 1% chance of a flood that bad." Is this description accurate or not? Explain.