The PDF of a General Function Covariance Correlation 1324 A Simple Example

The pdf of a general function covariance correlation

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The PDF of a General Function Covariance & Correlation 13/24 A Simple Example
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 13/24 A Simple Example p Y ( y ) = P ( g ( X ) = y ) = X x : g ( x )= y p X ( x )
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 14/24 A Linear Function of a Discrete r.v.
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 14/24 A Linear Function of a Discrete r.v. Linear Function Given Y = aX + b : p Y ( y ) = p X y - b a
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 15/24 A Linear Function of a Continuous r.v.
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 15/24 A Linear Function of a Continuous r.v. Linear Function Given Y = aX + b : f Y ( y ) = 1 | a | f X y - b a
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 16/24 A Linear Function of a Normal r.v. Definition Given X N ( μ, σ 2 ) and Y = aX + b f X ( x ) = 1 2 πσ e - ( x - μ ) 2 2 σ 2 Find f Y ( y )
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 17/24 The PDF of a General Function Definition Two-step procedure 1 Find the CDF of Y : F Y ( y ) = P ( Y y ) 2 Differentiate: f Y ( y ) = dF Y ( y ) dy
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 18/24 The PDF of a General Function
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Discrete R.V. Continuous R.V. The PDF of a General Function Covariance & Correlation 19/24 An Example X uniform on [0 , 2] , Y = X 3
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Covariance & Correlation 20/24 5-min Break!
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Probability & Statistics Calculation of normal probabilities Derived Distribu- tions Covariance & Correlation
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  • Fall '14
  • LuisDavidGarcia-Puente
  • Normal Distribution, Probability theory, probability density function, Covariance Properties, continuous random variable X

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