Page 129 - Applied statistics and probability for engineers

4

Continuous Random

Variables and

Probability

Distributions

The kinetic theory of gases provides a link between statis-
Chapter Outline tics and physical phenomena. The physicist James Maxwell
used some basic assumptions to determine the distribution
4-1 Continuous Random Variables of molecular velocity in a gas at equilibrium. As a result of
molecular collisions, all directions of rebound are equally
4-2 Probability Distributions and likely. From this concept, he assumed equal probabilities
Probability Density Functions for velocities in all the x, y, and z directions and inde-
4-3 Cumulative Distribution Functions pendence of these components of velocity. This alone is
sufi cient to show that the probability distribution of the
4-4 Mean and Variance of a Continuous velocity in a particular direction x is the continuous prob-
Random Variable ability distribution known as the normal distribution. This
fundamental probability distribution can be derived from
4-5 Continuous Uniform Distribution other directions (such as the central limit theorem to be dis-
cussed in a later chapter), but the kinetic theory may be the
4-6 Normal Distribution most parsimonious. This role for the normal distribution
4-7 Normal Approximation to the Binomial illustrates one example of the importance of continuous
and Poisson Distributions probability distributions within science and engineering.
4-8 Exponential Distribution

4-9 Erlang and Gamma Distributions

4-10 Weibull Distribution
4-11 Lognormal Distribution

4-12 Beta Distribution

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