Sampling Distributions

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Sampling Distribution Illustration

Central Limit Theorem

 

Let \(X_1,X_2,...,X_n\) have population mean \(\mu\) and variance \(\sigma^2\)

\[ \bar{X} \sim N(\mu,\frac{\sigma^2}{n}) \]

 

As the sample size gets large, the sample mean becomes normally distributed, with mean \(\mu\) and standard error \(\sigma/\sqrt{n}\) , regardless of the distribution of \(X_1,...,X_n\)