Created 3 years ago
MA2102
Probability and Statistics
Lecture-5
From the relative frequency definition we can observe three basic properties of chance,that are
i). Non-negativity property
ii). Certainty property
iii). If then
then
Additive property
Axiomatic definition of probability:
Let be a measurable space, a set function is called a probability(measure) function on if it satisfies the following axioms.
Axiom 1: (Non-negativity axiom)
Axiom 2: (Certainty axiom)
Axiom 3: For any sequence of events in such that for then,
(Countable additivity axiom)
Here the triple is called a probability space(or probability model)
Let be an index set,
- Collection of events in , are said to be mutually exclusive if for (At most on event in collection can occur when we performs an experiment which means no two events in the collection can happen simultaneously)
- Collection of events in , are said to be exhaustive if (At least one event in collection always occur when we performs an experiment)
- Collection of events in , are said to form a partition for if they are both mutually exclusive and exhaustive (Exactly one event in collection can occur when we performs an experiment)
In all of the following theorems we consider probability space