chapter 4 – continuous random variables and probability...
TRANSCRIPT
![Page 1: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/1.jpg)
Chapter 4 – Continuous Random Variables and Probability
Distributions
![Page 2: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/2.jpg)
Outline – Continuous random variables and probability density
functions
![Page 3: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/3.jpg)
Outline – Cumulative distribution function and expected values
![Page 4: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/4.jpg)
Outline – The normal distribution
![Page 5: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/5.jpg)
Outline – The Gamma distribution and its relatives
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Outline – Probability plots
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Continuous Random Variables
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Probability density function
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Uniform distribution
![Page 10: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/10.jpg)
Example 4.4
![Page 11: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/11.jpg)
The cumulative distribution function
![Page 12: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/12.jpg)
Computing probabilities using the cdf
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Example 4.6
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Percentiles of a continuous distribution
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Mean of a continuous random variable
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Example 4.9
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Example 4.9 continued
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Expected value of a function of a rv
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Example 4.10
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Variance of a continuous rv
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A shortcut formula for variance
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The normal distribution
![Page 23: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/23.jpg)
Normal density curves
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The standard normal distribution
![Page 25: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/25.jpg)
Nonstandard normal distribution
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The Gamma distribution
![Page 27: Chapter 4 – Continuous Random Variables and Probability ...people.stat.sfu.ca/~cao/Teaching/Stat285/chapter4.pdfProbability Distributions . Outline Continous random variables and](https://reader030.vdocuments.net/reader030/viewer/2022040223/5e53f1a1f99d4d0c40733875/html5/thumbnails/27.jpg)
Gamma density curves
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Probabilities from the gamma distribution
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The exponential distribution
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Exponential density curves
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The Chi-squared distribution
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Chi-squared densities