Question

What does statistically independent mean?

Answer 1

Statistically independent

1. In probability, statistically independent means that the occurrence of an event does not affect the chance of occurrence of another event.
2. Mathematically, this can be written as $\mathbf{P}\left(A\cap B\right)\mathbf{=}\mathbf{P}\left(A\right)\mathbf{·}\mathbf{P}\left(B\right)$
3. By conditional probability theorem $\mathbf{P}\left(\frac{A}{B}\right)\mathbf{=}\frac{\mathbf{P}\left(A\cap B\right)}{\mathbf{P}\mathbf{\left(}\mathbf{B}\mathbf{\right)}}\mathbf{=}\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{\right)}$.Thus, the occurrence of $A$ does not affect the probability of $B$, and vice versa.

Hence, the meaning of statistically independent is explained.