This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 σ5 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...
View
Full
Document
 Fall '10
 YingYingLi
 Business

Click to edit the document details