Random Samples and Central Limit Theorem

Random samples

• Considering having a large number

Central limit theorem

• if i have random samples taken from popultaion

  • the whole population has mean $\mu$ and variance ${\sigma }^2$

  • if $\bar{x}$ is the sample mean

    • then the limiting form of the distribution has
    • $Z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}$
      • as n → $inf$ then it follows theh standard normal distriubiton
        • the guassian PDF Ch 3 Probability