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# chapter9 - Chapter 9 Continuous Probability Distributions...

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Chapter 9 Continuous Probability Distributions In contrast to a discrete random variable, a continuous random variable is one that can assume an uncountable number of values, i.e we cannot list the possible values because there is an infinite number of them, and because there is an infinite number of values, the probability of each individual value is virtually 0. Hence, we cannot speak of P ( X = x ) for continuous random variable as we did for discrete random variables. Rather, we can determine the probability of a range of values only, say, P ( x 1 X x 2 ), where x 1 < x 2 . This is why we refer to a probability density function (p.d.f) as we had done for the normal distribution described in the earlier chapter. Note that the for every p.d.f, usually denoted f ( x ), whose range is a x b , 1) f ( x ) 0 for all x between a and b , and 2) the total area under the curve between a and b is 1 or 100%. 9.1 Uniform distribution The uniform probability distribution, sometimes called the rectangular probability distribution, is described by the function: 1

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