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Unformatted text preview: he distribution of the standardized random variable XσX X .
Solution The mean, µX , is the midpoint of the interval [a, b], and the standard deviation is
σX = (2−a) . The pdf for X − µX is obtained by shifting the pdf of X to be centered at zero.
Thus, X − µX is uniformly distributed over the interval [− b−a , b−a ]. When this random variable is
divided by σX , the resulting pdf is shrunk horizontally by the factor σX . This results in a uniform
distribution over the interval [− 2σX , 2σX ] = [− 3, 3]. This makes sense, because the uniform
distribution over the interval [− 3, 3] is the unique uniform distribution with mean zero and
variance one. 3.6. LINEAR SCALING OF PDFS AND THE GAUSSIAN DISTRIBUTION 3.6.2 89 The Gaussian (normal) distribution The Gaussian distribution, also known as the normal distribution, has the pdf
( u − µ) 2
f (u) = √
2πσ 2 , where the parameters are µ and σ 2 . The distribution is often denoted by “N (µ, σ 2 )...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- The Land