Chapter3 - Chapter 3 Probability Probability is the tool...

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Chapter 3 Probability Probability is the tool that allows the statistician to use sample information to make infer- ences about or to describe the population from which the sample was drawn. 3.1 Events, Sample Spaces, and Probability Defnition 3.1 Experiment: An experiment is the process by which an observation (or measurement) is obtained. Defnition 3.2 Sample Point: A sample point is the most basic outcome of an experiment. Defnition 3.3 Sample Space: The sample space is the set of all possible outcomes (sample points) of an experiment and is denoted by the symbol S . Example 3.1, page 118 : Two coins are tossed and their up faces are recorded. List of all sample points for this experiment. Find the sample space S. See examples for experiments and sample spaces in Table 3.1 on page 119. Extra Example 1 : Toss a fair coin and through a die. List of all sample points for this experiment and ±nd the sample space S. Venn Diagram: A pictorial method for presenting the sample space where each sample point is represented by a solid dot and labeled accordingly is called the Venn diagram. See Figure 3.2, page 120. Probability: The probability of a sample point is a number between 0 and 1 that measures the likelihood that the outcome will occur when the experiment is performed. Probability Rules For Sample Points: Let p i represent the probability of a sample point i . Then 1. All sample point probabilities must lie between 0 and 1 (0 p i 1). 2. The probabilities of all the sample points within a sample space must sum to 1 ( i p i = 1). Example 3.2, page 121. Example 3.3, page 122. 17
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Defnition 3.4 Event: An event is a specifc collection oF sample points. Simple Event: A single outcome oF an experiment is called a simple event. Compound Event: A compound event is a collection oF simple events. Probability oF an event: The probability oF an event A is equal to the sum oF the proba- bilities oF the simple events in A. Example 3.4, page 123 . Steps For calculating probabilities oF events 1. Defne the experiment 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.
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This note was uploaded on 09/15/2011 for the course STA 2023 taught by Professor Mcguckian during the Fall '08 term at FIU.

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Chapter3 - Chapter 3 Probability Probability is the tool...

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