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lesson4 - Discrete probability distribution

# lesson4 - Discrete probability distribution - Lesson4...

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson4-1 Lesson 4: Discrete Probability  Distributions

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson4-2 Outline Random variables and probability distribution Features of univariate probability distribution Binomial Probability Distribution Hypergeometric Probability Distribution Poisson Probability Distribution Features of bivariate probability distribution Conditional distribution Conditional expectation Covariance and Correlation Coefficient
Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson4-3 Random Variables and probability  distribution random variable  is a numerical value determined by the  outcome of an experiment.  A random variable is often  denoted by a capital letter, e.g., X or Y. A  probability distribution  is the listing of all possible  outcomes of an experiment  and  the corresponding probability.

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson4-4 Types of Probability Distributions discrete probability distribution  can assume only certain  outcomes (need not be finite) – for  random  variables that  take discrete values. The number of students in a class. The number of children in a family. continuous probability distribution  can assume an  infinite   number of values within a given range – for random  variables that  take continuous values . The time it takes an executive to drive to work. The amount of money spent on your last haircut. The distance students travel to class.
Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson4-5 Types of Probability Distributions Number of random variables Joint  distribution 1 Uni variate probability distribution 2 Bi variate probability distribution 3 Tri variate probability distribution n Multi variate probability distribution Probability distribution may be classified according to the  number of random variables it describes.

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Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson4-6 Discrete Random Variables Can only take on a countable number of values Examples:  Roll a die once Let  X  be the number of times “4” comes up   (then  X  could be 0, or 1 time) Roll a die twice Let  X  be the number of times “4” comes up   (then  X  could be 0, 1, or 2 times)
Ka-fu Wong  ©  2007 ECON1003: Analysis of Economic Data Lesson4-7 Discrete Random Variables Can only take on a countable number of values Examples:  Toss a coin once.     Let  X  be the number of heads        (then  X  = 0 or 1) Toss a coin 5 times.     Let  X  be the number of heads        (then  X  = 0, 1, 2, 3, 4, or 5)

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Ka-fu Wong  ©  2007
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