Standardized Average

Definition

For a sequence of Independent Random Variable $X_1,\dots ,X_n$ with Common Mean $\mu$, and variance ${\sigma }^2$ the standardized average is: $Z_n=(\frac{{\overline{X}}_n-\mu }{\frac{\sigma }{\sqrt{n}}})=\sqrt{n}(\frac{{\overline{X}}_n-\mu }{\sigma })$

• Standardized RV will always have $\mu =0,\sigma =1$