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Unformatted text preview: Outline The Joint Probability Density Function Statistics and Sampling Distributions Lecture 14 Chapter 4: Multivariate Variables and Their Distribution Michael Akritas Michael Akritas Lecture 14 Chapter 4: Multivariate Variables and Their Distribu Outline The Joint Probability Density Function Statistics and Sampling Distributions The Joint Probability Density Function Definition and Basic Properties Marginal Probability Density Functions Conditional Probability Density Functions Independence Statistics and Sampling Distributions Definitions and Examples Michael Akritas Lecture 14 Chapter 4: Multivariate Variables and Their Distribu Outline The Joint Probability Density Function Statistics and Sampling Distributions Definition and Basic Properties Marginal Probability Density Functions Conditional Probability Density Functions Independence I The pdf of a univariate r.v. X is a function f ( x ) such that probabilities are represented as areas under the curve. Michael Akritas Lecture 14 Chapter 4: Multivariate Variables and Their Distribu Outline The Joint Probability Density Function Statistics and Sampling Distributions Definition and Basic Properties Marginal Probability Density Functions Conditional Probability Density Functions Independence I The pdf of a univariate r.v. X is a function f ( x ) such that probabilities are represented as areas under the curve. I In the bivariate case, the pdf is a function of two arguments, f ( x , y ), which defines a surface in 3D, and probabilities are represented as volumes under this surface. Thus, Michael Akritas Lecture 14 Chapter 4: Multivariate Variables and Their Distribu Outline The Joint Probability Density Function Statistics and Sampling Distributions Definition and Basic Properties Marginal Probability Density Functions Conditional Probability Density Functions Independence I The pdf of a univariate r.v. X is a function f ( x ) such that probabilities are represented as areas under the curve. I In the bivariate case, the pdf is a function of two arguments, f ( x , y ), which defines a surface in 3D, and probabilities are represented as volumes under this surface. Thus, Definition The joint or bivariate density function of the continuous ( X , Y ) is a nonnegative function f ( x , y ) such that Michael Akritas Lecture 14 Chapter 4: Multivariate Variables and Their Distribu Outline The Joint Probability Density Function Statistics and Sampling Distributions Definition and Basic Properties Marginal Probability Density Functions Conditional Probability Density Functions Independence I The pdf of a univariate r.v. X is a function f ( x ) such that probabilities are represented as areas under the curve. I In the bivariate case, the pdf is a function of two arguments, f ( x , y ), which defines a surface in 3D, and probabilities are represented as volumes under this surface. Thus, Definition The joint or bivariate density function of the continuous ( X , Y ) is a nonnegative function f ( x , y ) such that...
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 Spring '00
 Akritas
 Statistics, Probability, Probability theory, probability density function, probability density, probability density functions, Michael Akritas

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