Lecture 5 - Chapter 5 Discrete Discrete Distributions...

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Unformatted text preview: Chapter 5 Discrete Discrete Distributions Distributions 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. 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 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 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 Some Special Distributions Discrete • binomial • Poisson • hypergeometric Continuous • normal • uniform • exponential • t • chi-square • F Discrete Distribution: Toss 2 coins 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 1 2 Number of heads Probability Discrete Distribution 1 2 3 4 5 0.37 0.31 0.18 0.09 0.04 0.01 Number of Crises Probability Distribution of Daily Crises 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 1 2 3 4 5 Number of crises Probability x P(x) xP(x) .37 .00 1 .31 .31 2 .18 .36 3 .09 .27 4 .04 .16 5 .01 .05 1.15 Mean of the Crises Data Example 0.0 0.1 0.2 0.3 0.4 0.5 1 2 3 4 5 Number of crises Probability ( 29 15 1 . P(x) x x E μ = ⋅ = = ∑ Variance and Standard Deviation...
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This note was uploaded on 08/22/2011 for the course FINC 2011 taught by Professor Craigmellare during the Three '10 term at University of Sydney.

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Lecture 5 - Chapter 5 Discrete Discrete Distributions...

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