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LectureNotes1 - Foundations of Probability: Part I Cyr...

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Unformatted text preview: Foundations of Probability: Part I Cyr Emile MLAN, Ph.D. mlan@stat.uconn.edu Foundations of Probability: Part I p. 1/36 Introduction Text Reference : Introduction to Probability and Its Application, Chapter 2. Reading Assignment : Sections 2.1-2.3, January 20-January 26 Uncertainty or chance variation can be found in nearly every aspect of our lives. For example, Will it rain tomorrow? Will the patient survive? How long will his illness last? Will the economy expand next year? How large a rain will I receive next year? Foundations of Probability: Part I p. 2/36 Introduction Even the best deterministic theory cannot give an accurate answer to these questions and an explanation for the variations that are observed. How can an inexact situation be studied? To aid, probability or chance is used to report and explain such variation. The method of probability makes precise the degree of predictability and further indicates the likelihood of occurrence of each possibility. Probability can be defined as a scientific discipline to study uncertainty in a systematic fashion. Foundations of Probability: Part I p. 3/36 Random Experiments Many experiments such as tossing a coin, rolling a dice, drawing a card, spinning a roulette wheel, counting the number of arrivals at emergency room, guessing tomorrow weather, measuring the lifetime of an bulb, etc... have unpredictable outcomes. We cannot say with absolute certainty which outcome will show up . Such experiment are called random experiment . A random experiment or a probability experiment is an action or process that leads to one of several possible outcomes and before it is performed, one cannot guess which outcome will come out. An outcome is a result of a random experiment. Examples Experiment: Record marks on a statistics test (out of 100). Outcomes: Numbers between 0 and 100 Experiment: Record student evaluations of a course. Outcomes: Poor, fair, good, very good, and excellent Foundations of Probability: Part I p. 4/36 Sample Space and Events Sample space A sample space, S , is the set that consists of all possible outcomes of a random experiment listed in a mutually exclusive and exhaustive way. A probability experiment consists in determining the gender of a new-born child. The sample space is S = { girl , boy } . A probability experiment consists of tossing a coin. The sample space is S = { H,T } . A probability experiment consists of tossing two coins simultaneously. The sample space is S = { ( H,H ) , ( H,T ) , ( T,H ) , ( T,T ) } . A probability experiment consists of rolling a regular six-sided die onto a table and recording the number on the upper face. The sample space is S = { 1 , 2 , 3 , 4 , 5 , 6 } ....
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LectureNotes1 - Foundations of Probability: Part I Cyr...

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