Independence Cont., Random Variables and Distributions

Class: STAT 131 Subject: probability Date: 2025-01-21 Teacher: Prof. Marcela

Independence Cont.

Independence of 3 Events

• Events $A$, $B$ and $C$ are said to be independent if all the following are true: $P(A\cap B)=P(A)P(B)$ $P(A\cap C)=P(A)P(C)$ $P(B\cap C)=P(B)P(C)$ $P(A\cap B\cap C)=P(A)P(B)P(C)$

Conditional Independence

• Events $A$ and $B$ are said to be conditionally independent given $E$ if: $P(A\cap B|E)=P(A|E)P(B|E)$

Random Variables and Distributions