Central+Limit+Theorem

Central Limit Theorem (Sums of Random Variables) (GWU EMSE-271)
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Two cases (pws)
 * 1) "mean of a sufficiently large number of independent random variables" .. can be approximated with Normal Distrbution
 * 2) With multiple variables, the mean of the sum can be approximated with Normal Distrbution (pws interpretation)
 *  Also, "with Multiple Variables: Var[ å i X i ] = å i Var[X i ] (when X 1, …, X n are independent random variables). Again not so for other functions" (EMSE 208, Fall 2010, Lecture 3, Sldie 49)

"In probability theory, the **central limit theorem** (**CLT**) states conditions under which the mean of a sufficiently large number of independent random variables , each with finite mean and variance, will be approximately normally distributed. The central limit theorem also requires the random variables to be identically distributed, unless certain conditions are met. Since real-world quantities are often the balanced sum of many unobserved random events, this theorem provides a partial explanation for the prevalence of the normal probability distribution. The CLT also justifies the approximation of large-sample statistics to the normal distribution in controlled experiments." - [|Wikipedia] [ Illustrated - [|Wikipedia]] [ Simulated - [|Download]]


 * Sources:**
 * Central limit theorem. (2010, January 12). In //Wikipedia, The Free Encyclopedia//. Retrieved 00:16, January 13, 2010, from []
 * EMSE 271, Fall 2009
 * EMSE 208, Fall 2010