FE507 – 1024

FE507 – 1024Probability on finite sample spacesFormal definitionsProbability spaceConditional ProbabilityLaw of total probability Independence Extra

Probability on finite sample spaces

Formal definitions

Probability space

Probability space is defined by (S,F,P) and satisfies:

F is a family of events
S is subsets
P is probability set function.
- Assigns numbers to events.

Assume we have two different probability measure, then we have:

\begin{matrix} P_{r P} (A) = 0.2 \\ P_{r P} (A) = 0.8 \\ P_{r Q} (A) = 0.3 \\ P_{r Q} (A) = 0.7 \end{matrix}

If A is an event, then. the complement of A is also an event
$\begin{matrix} i f A \in B \\ t h e n : \\ A^{∁} \in F \end{matrix}$

Union

If A and B are both events, then A Union B is also be an event.
$\begin{matrix} i f A_{1}, A_{2}, . . . \in F \\ t h e n : \\ \cup_{i = 1}^{\infty} A_{i} \in F \end{matrix}$

F $\sigma field$ on S.