Discrete probability distributions homework

GEO 370 Numerical Methods in Geography

Discrete probability distributions homework

Due Thurs. March 26

Please show all work, using attached pages where necessary.

Hurricanes

Below are data for the number of U.S. hurricane landfalls from 1851-2006.

Hurricane strikes in the United States, 1851-2006

Blake, Rappaport and Landsea, 2007

Annual landfallsNo. years

027

148

236

331

46

53

64

71

Total156

A. Investigating the observational data

1. Construct an eight-bin histogram for the number of landfalls. (4 pts).

2. Compute the relative frequency of each number of landfalls, and label each value onto the previous histogram chart. (3 pts.)

3. What is the sum of all of these relative frequencies? (1 pt.)

B. Constructing a discrete distribution

4. Use the observational data to construct a Poisson model for hurricane landfalls. Display the frequency data in a histogram, similar to your approach in problem 2. (10 pts.)

5. Compare the frequencies of hurricane landfalls from the Poisson distribution with the frequencies from the 156-year data record. Comment on whether the hurricane landfalls occurring year-to-year appear to be a purely random phenomenon. (4 pts.)