Strong law of large numbers

Description:

• States that the average of a sample will, with probability 1, converge to the mean of that distribution.
• Let $X_1,X_2,...$ be a sequence of independent and identically distributed random variables, each having a finite mean $\mu =E[X_i]$.
  • Then, with probability 1, $\frac{X_1+\cdot \cdot \cdot +X_n}{n}\to \mu$ as $n\to \infty$