Central limit theorem

Description:

• Based on Weak law of large numbers
• Let $X_1,X_2,...$ be a sequence of independent and identically distributed random variables, each having finite mean $E[X_i]=\mu$.
  • Then the distribution of any Sample, $\frac{X_1+...+X_n-n.\mu }{\sigma \sqrt{n}}$ tends to standard normal distribution as $n\to \infty$
• A good rule of thumb for a good approximation is when $n$ is 30
  • but when the sd is larger, we need more n to ensure

Distribution of sample mean

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