1.1 Probability Theory as the Study of Random Phenomena
One of the most striking features of the present day is the steadily increasing use of the ideas of probability theory in a wide variety of scientific fields, involving matters as remote and different as the prediction by geneticists of the relative frequency with which various characteristics occur in groups of individuals, the calculation by telephone engineers of the density of telephone traffic, the maintenance by industrial engineers of manufactured products at a certain standard of quality, the transmission (by engineers concerned with the design of communications and automatic control systems) of signals in the presence of noise, and the study by physicists of thermal noise in electric circuits and the Brownian motion of particles immersed in a liquid or gas. What is it that is studied in probability theory that enables it to have such diverse applications? In order to answer this question, we must first define the property that is possessed in common by phenomena such as the number of individuals possessing a certain genetical characteristic, the number of telephone calls made in a given city between given hours of the day, the standard of quality of the items manufactured by a certain process, the number of automobile accidents each day on a given highway, and so on. Each of these phenomena may often be considered a random phenomenon in the sense of the following definition.
