Chapter Three

Chapter Three - Lecture Notes Chapter Three: Probability...

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Lecture Notes Chapter Three: Probability Randall Miller 1 | Page 1. Events, Sample Spaces, and Probability Definition 3.1 An experiment is an act or process of observation that leads to a single outcome that cannot be predicted with certainty. Definition 3.2 A sample point is the most basic outcome of an experiment. Definition 3.3 The sample space of an experiment is the collection of all its sample points. Probability Rules for Sample Points Let p 1 represent the probability of sample i 1. All sample point probabilities must lie between 0 and 1 (i.e., 01 i p ≤≤ ) 2. The probabilities of all the sample points within a sample space must sum to 1 (i.e., 1 1 n i i p = = ) Definition 3.4 An event is a specific collection of sample points. Probability of an Event The probability of an even A is calculated by summing the probabilities of the sample points in the sample space for A . Steps for Calculating Probabilities of Events 1. Define the experiment; that is, describe the process used to make an observation and the type of observation that will be recorded. 2. List the sample points. 3. Assign probabilities to the sample points. 4. Determine the collection of sample points contained in the event of interest. 5. Sum the sample point probabilities to get the probability of the event.

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Lecture Notes Chapter Three: Probability Randall Miller 2 | Page Combinations Rule Suppose a sample of n elements is to be drawn from a set of N elements. Then the number of different sample possible is denoted by N n    and is equal to ( ) ! !! N n N N C n nN n = = where ( )( ) ( )( )( ) ! 1 2 ... 3 2 1 n nn n =−− and similarly for N ! and ( N n )! For example, 5! = 5 ·4·3·2·1. [ Note : The quantity of 0! is defined to be equal to 1.] 2. Unions and Intersections An event can often be viewed as a composition of two or more other events. Such events, which are called compound events , can be formed in two ways.
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This note was uploaded on 07/23/2011 for the course STA 3123 taught by Professor Staff during the Fall '08 term at FIU.

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Chapter Three - Lecture Notes Chapter Three: Probability...

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