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

4-7 Normal Approximation to the Binomial and Poisson Distributions

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 ...

Start Free Trial

No credit card required