Lecture 5 - Chapter5 Discrete Distributions...

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Chapter 5 Discrete Discrete Distributions Distributions
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Learning Objectives Distinguish between discrete random variables  and continuous random variables. Know how to determine the mean and variance of  a discrete distribution. Apply binomial distributions appropriately to solve  practical problems.  Decide when to use the Poisson distribution in  analyzing statistical experiments, and know how  to solve such problems.
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Learning Objectives  —  continued Decide when binomial distribution problems can  be approximated by the Poisson distribution, and  know how to solve such problems. Calculate expected value and variance of linear  combinations of random variables Calculate the covariance and understand its use  in finance
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Introduction to Probability  Distributions Random Variable —  a variable which contains (denotes)  the outcomes of a chance experiment Random Variables Discrete Random Variable Continuous Random Variable
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Discrete vs Continuous  Distributions Discrete Random Variable —  the set of all possible  values is at most a finite or a countably infinite number  of possible values Number of new subscribers to a magazine Number of bad cheques received by a restaurant Number of absent employees on a given day Continuous Random Variable —  takes on values at  every point over a given interval Current Ratio of a motorcycle distributorship Elapsed time between arrivals of bank customers Percent of the labor force that is unemployed
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Some Special Distributions Discrete binomial Poisson hypergeometric Continuous normal uniform exponential t chi-square F
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Discrete Distribution:  Toss 2 coins 0 1 2 0.25 0.50 0.25 Number of Heads Probability Distribution of Heads 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0 1 2 Number of heads Probability
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