Applied Statistics and Probability for Engineers, 6th Edition

Continuous Random Variables and Probability Distributions

Chapter Outline

4-1 Continuous Random Variables

4-2 Probability Distributions and Probability Density Functions

4-3 Cumulative Distribution Functions

4-4 Mean and Variance of a Continuous Random Variable

4-5 Continuous Uniform Distribution

4-6 Normal Distribution

4-7 Normal Approximation to the Binomial and Poisson Distributions

4-8 Exponential Distribution

4-9 Erlang and Gamma Distributions

4-10 Weibull Distribution

4-11 Lognormal Distribution

4-12 Beta Distribution

The kinetic theory of gases provides a link between statistics and physical phenomena. The physicist James Maxwell used some basic assumptions to determine the distribution of molecular velocity in a gas at equilibrium. As a result of molecular collisions, all directions of rebound are equally likely. From this concept, he assumed equal probabilities for velocities in all the x, y, and z directions and independence of these components of velocity. This alone is sufficient to show that the probability distribution of the velocity in a particular direction x is the continuous probability distribution known as the normal distribution. This fundamental probability distribution can be derived from other directions (such as the central limit theorem to be discussed ...