Handout_4 Introduction to probability

Handout_4 Introduction to probability - Feb 909...

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Feb 9’09 INTRODUCTION TO PROBABILITY #4 The theory of probability provides the foundation for statistical inference . BASIC TERMS . In probability, an experiment is an activity or occurrence with an observable result. Each repetition of an experiment is called a trial . The possible results of each trial are called outcomes or events . The set of all possible outcomes for an experiment is called the sample space for that experiment. For example, a sample space S for the experiment of tossing a coin is made up of two possible outcomes: heads ( h ) and tails ( t ) . In the set notations, we may write S = {h, t} An event is a subset of a sample space . Events are designated with capital letters: A, B, …, E, … which may have subscripts. Thus, in the experiment of tossing a coin, one of two mutually exclusive events may occur: the event A = {h} , which represents the outcome “heads” and the event B = {t} , which represents the outcome “tails”. ( The events are said to be mutually exclusive if no two of them can occur together ). Different types of events may be associated with the same experiment, and an experiment may have more than one sample space associated with it . Example : for the experiment of rolling a single fair six-sided die, if we consider the events like showing a single number on the top face, then we may introduce a sample space (of size 6) S = {1, 2, 3, 4, 5, 6} which includes six possible mutually exclusive outcomes. But we may associate with this experiment also some other events: a) the die shows an odd number : there are three possible events of this type: E 1a = {1}, E 2a = {3}, E 3a = {5}, and the corresponding sample space (of size 3) is S a = {1, 3, 5}; b) the die shows a number greater than 2 : there are four possible events of such a type: E 1b = {3}, E 2b = {4}, E 3b = {5}, E 4b = {6}, and the corresponding sample space (of size 4) is S b = {3, 4, 5, 6}; c) the die shows a multiple of 3 : there are two possible events of this type: E 1c = {3} and E 2c = {6}, and the sample space (of size 2) is S c = {3, 6}. A probability of an event

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This note was uploaded on 11/24/2011 for the course MATH 3000 taught by Professor Kzaer during the Spring '05 term at St. Johns College MD.

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Handout_4 Introduction to probability - Feb 909...

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