Agraphoftheprobabilitydensityfuntionisbelow fx 2 1 0

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Unformatted text preview: e uniform distribution over the interval [ x min , x max ] has the PDF: 1 ⎧ for x min < x < x max ⎪x − x min f(x ) = ⎨ max ⎪ 0 otherwise ⎩ For example, consider the uniform distribution over the interval [ 1 4 , 3 4] . A graph of the probability density funtion is below: f(x) 2 1 0 0 1/4 1/2 3/4 x Again, note that the total area under the PDF is equal to one. 4 Chapter 6 By comparing the graphs of the PDFs for the uniform distribution over the interval [0, 1] and the uniform distribution over [ 1 4 , 3 4] it can be seen that both are centered at 1 2 . However, the two distributions have different dispersion. That is, the PDF for the uniform distribution over [ 1 4 , 3 4] has a higher peak to suggest smaller dispersion. 5 Chapter 6 Example: Exercise 6.6, page 193 An emergency rescue team operates on a 4‐mile stretch of river. Let the random variable X be the distance (in miles) of an emergency from the northernmost point of this stretch of river. X follows a uniform distribution over the interval [0, 4] with PDF: ⎧ 0.25 for 0 < x < 4 ⎪ f(x ) = ⎨ ⎪ 0 otherwise ⎩ Selected questions and answers: (c) Find the probability that a given emergency arises within one mile of the northernmost point of this stretch of river. A graph of the PDF is shown: f(x) Area = P(X < 1) = F(1) 0.25 0 0 1 2 3 4 x The area of a box is calculated as: (h...
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