A link between statistics and physical phenomena is provided by the kinetic theory of gases. 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 also 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 in a later chapter), but the kinetic theory may be the most parsimonious. This role for the normal distribution illustrates one example of the importance of continuous probability distribution distributions within science and engineering.

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

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