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Uniform

Uniform - y f(y 0.0 0.2 0.4 0.6 0.8 1.0 0.8 0.9 1.0 1.1 1.2...

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Uniform Distribution The uniform distribution is used to model continuous data when the probability histogram is approximately a horizontal line throughout the range of the data. The uniform distribution has the following properties: The parameters of the uniform distribution are the minimum ( θ 1 ) and maximum ( θ 2 ) value. The standard uniform distribution has minimim θ 1 = 0 and maximum θ 2 = 1 . The probability density function for the uniform distribution is f ( y ) = 1 θ 2 - θ 1 θ 1 y θ 2 The distribution function for the uniform distribution is F ( y ) = P ( Y y ) = 0 y < θ 1 y - θ 1 θ 2 - θ 1 θ 1 y θ 2 1 y > θ 2 Here are graphs of the probability density function and distribution function of a Uniform distribution with θ 1 = 0 and θ 2 = 1. p.d.f. of Uniform distribution with min = 0 and max = 1

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Unformatted text preview: y f(y) 0.0 0.2 0.4 0.6 0.8 1.0 0.8 0.9 1.0 1.1 1.2 Distribution of Uniform distribution with min = 0 and max = 1 y F(y) 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 • The theoretical mean of the uniform distribution is μ = E ( Y ) = θ 1 + θ 2 2 • The variance of the uniform distribution is σ 2 = V ( Y ) = ( θ 2-θ 1 ) 2 12 Working with uniform random variables in R. To Fnd the probability P ( Y ≤ y ), the command in R is 1 punif(y,a,b) To fnd the value oF y so that P ( Y ≤ y ) = p , the command in R is qunif(p,a,b) To generate observed values From a uniForm distribution, the command in R is runif(numobs,a,b) where numobs is the number oF observed values you would like to generate. 2...
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Uniform - y f(y 0.0 0.2 0.4 0.6 0.8 1.0 0.8 0.9 1.0 1.1 1.2...

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