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Unformatted text preview: Chapter 5 Continuous Random Variables 5.1 Probability Distributions for Continuous Random Variables Continuous Random Variable : A continuous random variable (RV) is one that can assume the infinitely many values corresponding to the points on a line interval. For examples i. The heights or weights of a group of people. ii. The life time of a battery. iii. The time between service calls on an oce machine. Unlike discrete random variables, we can not assign a positive probability to each of these infinitely many points and still have the probabilities sum to 1. Probability Density Function ( pdf ): The density function f ( x ), represented graphically in figure (5.1, page 206), provides a mathematical model for the population relative frequency histogram that exists in reality. The total area under the curve is always 1. The probability that a continuous random variable assumes a value in the interval a to b is the area under the probability density function between the points a and b . For example, see figure 5.1, page 206....
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