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Probability - Basic Concepts

Random Process: Any process whose possible results are known but whose actual results cannot be predicted with certainty in advance.

Outcome: Each possible result for a random process.

Experiment: A procedure used to generate outcomes (or make measurements) from a random process.

Sample Space (S): The set of all possible outcomes from an experiment.

Event: Any subset of the sample space.

Note: The entire sample space S is an event too.

The union of events E1 and E2 (denoted E1ÈE2) is the event consisting of all outcomes contained in at least one of E1 or E2. Thus the union of some collection of events E1, E2,... denoted by Èi(Ei) is the event consisting of all outcomes contained in at least one of  the events Ei.

The intersection of events E1 and E2 (denoted E1ÇE2) is the event consisting of all outcomes contained in both E1 and E2. Thus the intersection of some collection of events E1, E2,... denoted by Çi(Ei) is the event consisting of all outcomes contained in every one of the events Ei.

The complement of an event Ei (denoted by Ei¢) is the set of all outcomes not in Ei.

Disjoint or Mutually Exclusive events E1 and E2 have no outcomes in common, i.e., E1Ç E2 = f . This implies that the events E1 and E2 can never happen simultaneously.

A probability measure P(·) is a set function that assigns to any event E the real number P(E) called the probability of E which is a precise measure of the likelihood of the event E occurring.

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Jayant Rajgopal