Chapter 5.1, Problem 13E

Major Hurricanes. The Atlantic Hurricane Database extends back to 1851, recording among other things the number of major hurricanes striking the U.S. Atlantic and Gulf Coast per year. A major hurricane is a hurricane measuring at least a Category 3 on the Saffir-Simpson hurricane wind scale (i.e., with winds of at least 110 mph). As published by the National Oceanic & Atmospheric Administration and the Atlantic Oceanographic & Meteorological Laboratory, the following table provides a probability distribution for the number of major hurricanes, Y, for a randomly selected year between 1851 and 2012.

Use random-variable notation to represent each of the following events. The year had

1. a. at least one major hurricane.
2. b. exactly three major hurricanes.
3. c. between 2 and 4 major hurricanes, inclusive. Use the special addition rule and the probability distribution to determine
4. d. P(Y ≥ 1).
5. e. P(Y = 3).
6. f. P(2 ≤ Y ≤ 4).