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Probability

5.9 The Multivariate Normal Distribution

Alex Tsun

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Agenda

  • Covariance Matrices
  • The Special Case of Independent Normals
  • The Bivariate Normal Distribution
  • The Multivariate Normal Distribution

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Covariance Matrices

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Covariance Matrices

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Covariance Matrices

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Covariance Matrices

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Covariance Matrices

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Covariance Matrix (Example)

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Covariance Matrix (Example)

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Properties

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Random Picture

Definition of

Expectation

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The Special Case of Independent Normals

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The Special Case of Independent Normals

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The Special Case of Independent Normals

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The Bivariate Normal Distribution

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The Bivariate Normal Distribution

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The Bivariate Normal Distribution

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The Bivariate Normal Distribution

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The Bivariate Normal Distribution

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The Bivariate Normal Distribution

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Bivariate Normal Density

Definition of

Expectation

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Bivariate Normal Covariance Intuition

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The Multivariate Normal Distribution

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The Multivariate Normal Distribution

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The Multivariate Normal Distribution

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END PIC

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Alex Tsun

Joshua Fan