Probability Measure

Description

Simulate the Probability measure.

The probability measure {\displaystyle P}P is a set function returning an event's probability. A probability is a real number between zero (impossible events have probability zero, though probability-zero events are not necessarily impossible) and one (the event happens almost surely, with almost total certainty). Thus P is a function P:F→[0,1] .

Probability measure definition - Wiki or in the context of Probability Space defined here

Reference

   from probnode import P__

Or, alternatively,

   from probnode import ProbabilityMeasureOfEvent

Constructor	Description	Link
Probability measure: P__(random_variable: RandomVariable)	Initialize Probability measure (for example: p_X = P__(random_variable) with defined Random variable. Passing event to the Probability measure will return the Probability measure on the event, p_X(event) (equals ProbabilityMeasureOfEvent(event, random_variable)	basic
Probability measure of specified event: ProbabilityMeasureOfEvent(event: BaseEvent, random_variable: RandomVariable)	Create a determined, or encased Probability measure with defined Random variable on specified Event.	basic

Some insights

Given that the σ-algebra F is a collection of all the events we would like to consider. A Probability measure (is a function P:F → [0,1] ) , alone, does not specify which Sample space Ω it operating on, thus cannot be used to interpret Event.

A Probability measure belonging to a Probability space, a mathematical triplet (Ω,F,P) , or in other word, belonging to a Random variable X:Ω→R( The technical axiomatic definition requires Ω to be a sample space of a probability triple (Ω,F,P) (see the measure-theoretic definition) ), can thus be useful as a function to interpret Event

Characteristics

If the Random variable is not specified, or cannot determine the probability of the event, the probability value (get by eval_p(p_x)) will return as None