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# Normal - 0.4 Distribution of Normal distribution with mean...

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Normal Distribution A normal distribution is used to model continuous data when the probability histogram has an approximate bell-shape. The normal distribution has the following properties: The parameters for the normal distribution are the mean μ and the variance σ 2 . The standard normal distribution has mean μ = 0 and variance σ 2 = 1. The probability density function for the normal distribution is f ( y ) = 1 σ 2 π e - ( y - μ ) 2 2 σ 2 - ∞ < y < The distribution function F ( y ) for the normal distribution does not have a closed form so- lution. You must use tables or a computer package to find probabilities associated with the normal distribution. Here are graphs of the probability density function and distribution function of a Normal distribution with μ = 0 and σ 2 = 1. p.d.f. of Normal distribution with mean = 0 and variance = 1 y f(y) -4 -2 0 2 4 0.0 0.1 0.2

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Unformatted text preview: 0.4 Distribution of Normal distribution with mean = 0 and variance = 1 y F(y)-4-2 2 4 0.6 0.8 1.0 • The theoretical mean of the normal distribution is μ = E ( Y ) = μ • The variance of the normal distribution is σ 2 = V ( Y ) = σ 2 • The normal distribution is very important in statistical theory and we will be learning much more about this distribution in Statistics 342. Working with normal random variables in R. To Fnd the probability P ( Y ≤ y ) the command in R is pnorm(y,mu,sigma) 1 To fnd the value oF y so that P ( Y ≤ y ) = p the command in R is qnorm(p,mu,sigma) To generate observed values From a normal distribution the command in R is rnorm(numobs,mu,sigma) where numobs is the number oF observed values you would like to generate. 2...
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