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Unformatted text preview: Outline Models for Continuous RVs – The Normal Distribution Distribution Models Used in Reliability Lecture 12 Chapter 3: Random Variables and Their Distributions Michael Akritas Michael Akritas Lecture 12 Chapter 3: Random Variables and Their Distributio Outline Models for Continuous RVs – The Normal Distribution Distribution Models Used in Reliability Models for Continuous RVs – The Normal Distribution Definition: The pdf and cdf Basic Property of the Normal Distribution Finding Probabilities via the Standard Normal Table Finding Percentiles via the Standard Normal Table Distribution Models Used in Reliability Terminology Used in Reliability The Lognormal distribution The Gamma and the χ 2 distributions The Weibull distribution Michael Akritas Lecture 12 Chapter 3: Random Variables and Their Distributio Outline Models for Continuous RVs – The Normal Distribution Distribution Models Used in Reliability Definition: The pdf and cdf Basic Property of the Normal Distribution Finding Probabilities via the Standard Normal Table Finding Percentiles via the Standard Normal Table A random variable X is said to have the normal distribution with parameters μ and σ , denoted by X ∼ N ( μ,σ 2 ), if its pdf is f ( x ; μ,σ 2 ) = 1 √ 2 πσ 2 e ( x μ ) 2 2 σ 2 ,∞ < x < ∞ . Michael Akritas Lecture 12 Chapter 3: Random Variables and Their Distributio Outline Models for Continuous RVs – The Normal Distribution Distribution Models Used in Reliability Definition: The pdf and cdf Basic Property of the Normal Distribution Finding Probabilities via the Standard Normal Table Finding Percentiles via the Standard Normal Table A random variable X is said to have the normal distribution with parameters μ and σ , denoted by X ∼ N ( μ,σ 2 ), if its pdf is f ( x ; μ,σ 2 ) = 1 √ 2 πσ 2 e ( x μ ) 2 2 σ 2 ,∞ < x < ∞ . f(x)321 1 2 3 0.0 0.1 0.2 0.3 0.4 mu=0, sigm^2=1 mu Michael Akritas Lecture 12 Chapter 3: Random Variables and Their Distributio Outline Models for Continuous RVs – The Normal Distribution Distribution Models Used in Reliability Definition: The pdf and cdf Basic Property of the Normal Distribution Finding Probabilities via the Standard Normal Table Finding Percentiles via the Standard Normal Table The Standard Normal Distribution Michael Akritas Lecture 12 Chapter 3: Random Variables and Their Distributio Outline Models for Continuous RVs – The Normal Distribution Distribution Models Used in Reliability Definition: The pdf and cdf Basic Property of the Normal Distribution Finding Probabilities via the Standard Normal Table Finding Percentiles via the Standard Normal Table The Standard Normal Distribution When μ = 0 and σ = 1, X is said to have the standard normal distribution and is denoted, universally, by Z ....
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This note was uploaded on 03/19/2009 for the course STAT 401 taught by Professor Akritas during the Spring '00 term at Penn State.
 Spring '00
 Akritas
 Normal Distribution

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