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Uncertainty or variability are prevalent in many situations and it is the purpose of the probability theory to understand and quantify this notion. The basic FELLER - An Introduction to Probability Theory and Its Applica- tions, VolumeIT. FISZ + Probability Theory and Mathematical Statistics, Third Edition.Probability theory provides a mathematical foundation to concepts such as Example: For a continuous uniform [a, b] random variable X, the pdf is as fol-. This book on probability theory and mathematical statistics is designed for The function f is called the probability density function (PDF) of the RV X.