chap6A - Chapter6 interval. interest

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Chapter 6 Continuous Random Variables A continuous random variable can take any numerical value in some interval. Assigning probabilities to individual values is not possible. Probabilities can be measured in a given range. For a continuous random variable X with a numerical value of interest x the cumulative distribution function ( CDF ) is denoted by: with ) x X ( P ) x X ( P ) x ( F < = = 0 ) x X ( P = = For two numerical values a and b , with a < b , the probability that the outcome is in a range is: ) a ( F ) b ( F ) a X ( P ) b X ( P ) b X a ( P ) b X a ( P = < < = = < < Chapter 6 1
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The probability density function ( PDF ) is given by: for all values of x . 0 ) x ( f > The properties of a probability density function can be illustrated with a special distribution called the uniform distribution . The uniform distribution over the interval [0, 1] has the PDF: < < = otherwise 1 x 0 for 0 1 ) x ( f A graph of the probability density function is below. 1 0 1 a 0 f(x) x Area = P(X < a) = F(a) Chapter 6 2
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