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LectureNotes4 - Probability: Part I Cyr Emile MLAN, Ph.D....

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Probability: Part I Cyr Emile M’LAN, Ph.D. mlan@stat.uconn.edu Probability: Part I – p. 1/31
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Introduction Text Reference : Introduction to Probability and Statistics for Engineers and Scientists, Chapter 3. Reading Assignment : Sections 3.1-3.5, September 17-September 22 In chapter 2, we introduced graphical and numerical descriptive methods. Although these tools are useful to understand the structure of variability in a given data, one is particularly interested in developing statistical inference. Statistical inference is the process by which one acquires information about a population from samples. A critical component of statistical inference is probability because it provides the link between the population and the sample. Probability permits one to make inference from a sample to the population and in addition to measure how accurate and reliable the inference is. Probability: Part I – p. 2/31
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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 an 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 Probability: Part I – p. 3/31
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Sample Space and Events Sample space A sample space, S , is the set that consists of all possible outcomes of an experiment. — 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 selecting a faculty member at Uconn and recording her income. The sample space is S = [0 , ) . — A probability experiment consists of selecting 5 faculty members at Uconn and recording their incomes. The sample space is S = [0 , ) 5 . Probability: Part I – p. 4/31
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Sample Space and Events A sample space is said to be discrete if it contains either a finite or a countable number of distinct sample points. — A probability experiment consists of tossing a coin
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LectureNotes4 - Probability: Part I Cyr Emile MLAN, Ph.D....

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