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Random Sample's Sample Mean Average and Variance 📂Mathematical Statistics

Random Sample's Sample Mean Average and Variance

Formulas

Given a random sample X1,⋯ ,Xn∼iidXX_{1} , \cdots , X_{n} \overset{\text{iid}}{\sim} X, the mean and variance of its sample mean Xˉ\bar{X} are as follows. EXˉ=EXVar⁡Xˉ=1nVar⁡X \begin{align*} E \bar{X} =& E X \\ \operatorname{Var} \bar{X} =& {{ 1 } \over { n }} \operatorname{Var} X \end{align*}