# Pairwise Independence vs Idependence help

• Sep 15th 2009, 01:59 PM
diddledabble
Pairwise Independence vs Idependence help
Okay. I have search the internet over for independence in probability and all I get is pairwise examples. I am trying to figure out exactly what the difference is. For example, what would the formula be to find the $P(A\cup B\cup C)$ Does it differ from pairwise independence too just finding indepence?
• Sep 15th 2009, 02:50 PM
Plato
Quote:

Originally Posted by diddledabble
Okay. I have search the internet over for independence in probability and all I get is pairwise examples. I am trying to figure out exactly what the difference is. For example, what would the formula be to find the $P(A\cup B\cup C)$ Does it differ from pairwise independence too just finding indepence?

Here is a standard example.
Toss a coin twice.
$\mathcal{A}$ is the event that the first toss yeilds heads.
$\mathcal{B}$ is the event that the second toss yeilds heads.
$\mathcal{C}$ is the event that both tosses match (two heads or two tails).

You can show that $\mathcal{A}~\&~\mathcal{B}$, $\mathcal{A}~\&~\mathcal{C}$, and $\mathcal{C}~\&~\mathcal{B}$ are all independent: Pair-wise independence.

But these are not mutually independent: $P\left(\mathcal{A}\mathcal{B}\mathcal{C}\right)\ne P(\mathcal{A})P(\mathcal{B})P(\mathcal{C})$