Class Meeting 06

# Class Meeting 06 - CHEN 3010 Applied Data Analysis Class...

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1 CHEN 3010 Applied Data Analysis Class Meeting #6 September 9, 2003 Today's Topic The Normal Distribution Reading for Tuesday: pages 76-89 Homework #2 due today Homework #3 posted, due next Thursday Continuous Probability Distributions Lognormal Distribution Gamma & Weibull Distributions

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2 The Normal Distribution Normal density function ( ) ( ) 2 2 2 11 2 x f x e for x µ σ π = −∞ < < ∞ 0 µ= 1 σ= Standard normal density function ( ) 2 2 1 2 x f x e for x = −∞ < < ∞ 2 ) ( ) ( = = X V and X E
3 3-5 Important Continuous Distributions 3-5.1 Normal Distribution

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4 Standard Normal Distribution 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 x f(x)
5 Standard Normal Distribution 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 x f(x) 0.683 68.3% (about 2/3) of values fall within 1 ± σ

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6 Standard Normal Distribution 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 x f(x) 0.955 95.5% of values fall within 2 ± σ
7 Standard Normal Distribution 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 x f(x) 0.997 99.7% of values fall within 3 ± σ

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8 Probability calculations with the normal distribution
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Class Meeting 06 - CHEN 3010 Applied Data Analysis Class...

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