Applied Statistics and Probability for Engineers, 6th Edition

Joint Probability Distributions

Chapter Outline

5-1 Two or More Random Variables

5-1.1 Joint Probability Distributions

5-1.2 Marginal Probability Distributions

5-1.3 Conditional Probability Distributions

5-1.4 Independence

5-1.5 More Than Two Random Variables

5-2 Covariance and Correlation

5-3 Common Joint Distributions

5-3.1 Multinomial Probability Distribution

5-3.2 Bivariate Normal Distribution

5-4 Linear Functions of Random Variables

5-5 General Functions of Random Variables

5-6 Moment Generating Functions

Air-quality monitoring stations are maintained throughout Maricopa County, Arizona and the Phoenix metropolitan area. Measurements for particulate matter and ozone are measured hourly. Particulate matter (known as PM10) is a measure (in μg/m³) of solid and liquid particles in the air with diameters less than 10 micrometers. Ozone is a colorless gas with molecules comprised of three oxygen atoms that make it very reactive. Ozone is formed in a complex reaction from heat, sunlight, and other pollutants, especially volatile organic compounds. The U.S. Environmental Protection Agency sets limits for both PM10 and ozone. For example, the limit for ozone is 0.075 ppm. The probability that a day in Phoenix exceeds the limits for PM10 and ozone is important for compliance and remedial ...