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Applied Statistics and Probability for Engineers, 6th Edition by George C. Runger, Douglas C. Montgomery

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Continuous Random Variables and Probability Distributions

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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 ...

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