Lecture11 - lecture 11, Continuous Random Variable II 1/33...

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Unformatted text preview: lecture 11, Continuous Random Variable II 1/33 Normal Probability Distribution Computing Ar- eas/Probabilities for Standard Normal Connections between Std Normal and General Normals lecture 11, Continuous Random Variable II Outline 1 Normal Probability Distribution 2 Computing Areas/Probabilities for Standard Normal 3 Connections between Std Normal and General Normals lecture 11, Continuous Random Variable II 2/33 Normal Probability Distribution Computing Ar- eas/Probabilities for Standard Normal Connections between Std Normal and General Normals lecture 11, Continuous Random Variable II Normal Probability Distribution Normal Probability Distribution The normal probability distribution with mean μ and standard deviation σ , denoted by N ( μ,σ 2 ) , has density function f ( x ) = 1 √ 2 πσ 2 e- ( x- μ ) 2 2 σ 2 for all values x on the real number line • π ≈ 3 . 14159, and e ≈ 2 . 71828 is the base of natural logarithms • μ is the mean and σ is the standard deviation lecture 11, Continuous Random Variable II 3/33 Normal Probability Distribution Computing Ar- eas/Probabilities for Standard Normal Connections between Std Normal and General Normals lecture 11, Continuous Random Variable II Normal Probability Distribution Normal Probability Distribution with Different μ and σ-5 5 10 15 0.0 0.1 0.2 0.3 0.4 Normal Distributions with different mu and sigma x f(x) Normal(0,1) Normal(2,1) Normal(0,9) Normal(6,9) lecture 11, Continuous Random Variable II 4/33 Normal Probability Distribution Computing Ar- eas/Probabilities for Standard Normal Connections between Std Normal and General Normals lecture 11, Continuous Random Variable II Normal Probability Distribution Properties The Normal curve is symmetric about μ , and the total area under the curve equals 1. lecture 11, Continuous Random Variable II 5/33 Normal Probability Distribution Computing Ar- eas/Probabilities for Standard Normal Connections between Std Normal and General Normals lecture 11, Continuous Random Variable II Normal Probability Distribution Properties, ctd • The curve is symmetric about its center • Center=Mean = Median Mode: The mode of a continuous probability distribution is a point x at which its density function attains its maximum value. • For normal distributions, Center=Mean = Median = Mode lecture 11, Continuous Random Variable II 6/33 Normal Probability Distribution Computing Ar- eas/Probabilities for Standard Normal Connections between Std Normal and General Normals lecture 11, Continuous Random Variable II Normal Probability Distribution Properties ctd : Position and Shape • The mean μ positions the peak of the normal curve over the real number line • The sd σ measures the width or spread of the normal curve lecture 11, Continuous Random Variable II 7/33 Normal Probability Distribution Computing Ar- eas/Probabilities for Standard Normal Connections between Std Normal and General Normals lecture 11, Continuous Random Variable II Normal Probability Distribution...
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Lecture11 - lecture 11, Continuous Random Variable II 1/33...

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