Sampling Distributions, CLT

Standard Error

• different samples from same population are slightly different
  • calculate variance of sample means
• sample mean $\bar{x}$ is a good estimator of population mean $\mu$ $E[{\bar{x}}_n]=E[\frac{1}{n}{\sum }_{i=1}^n{x}_i]=\frac{1}{n}{\sum }_{i=1}^{n}E[x_i]=\mu$ $\mu =\frac{1}{n}\ast n\ast \mu =E[{\bar{x}}_n]$
• SE is standard deviation of $\bar{x}$
  • calculate variance of ${\bar{x}}_n$
  • todo copy from handwritten notes

Central Limit Theorem

• Central Limit Theorem