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Unformatted text preview: t follow the normal distribution – they may fit askewed distribution or any other non‐normal distribution. 2 Consider the sample mean: 1n
X = ∑ Xi n i=1 Earlier lecture notes stated the standard error of X as: se( X ) = σ n Define the standardized random variable: Z= X−μ X−μ =
se( X ) σ
n The Central Limit Theorem states that as n becomes ‘large’ the distribution of Z approaches the standard normal distribution. That is, Z ~ N(0 , 1) . Therefore, a random variable that can be viewed as the sum of a ‘large’ number of independently and identically distributed random variables will tend to have a normal distribution. 12 Chapter 7 A computer simulation can be used to demonstrate the Central Limit Theorem. Consider a random variable that follows the uniform distribution over the interval [0, 10] . A graph of the probability density function is below. 1/10 0 13 5 10 Chapter 7 A statistical result is that the average of two (n=2) independent uniform random variables has a tr...
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- Spring '10