probability and statistics with...
TRANSCRIPT
![Page 1: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/1.jpg)
Probability and Statistics with Programming
Course Code 009959 (Spring 2018)
Prof. S. M. Riazul Islam, Dept. of Computer Engineering, Sejong University, Korea
Joint Probability Distributions
E-mail: [email protected]
![Page 2: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/2.jpg)
Probability Distributions in R
Concepts of Joint Probability Distributions
Expected Values, Covariance, and Correlation
Central Limit Theory
![Page 3: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/3.jpg)
Joint Probability Distributions
Concepts of Joint Distribution
0-20 21-40 41-60 >60 Total
80-100 0% 2% 8% 10% 20%
60-79 0% 10% 15% 5% 30%
40-59 1% 2% 16% 16% 35%
20-39 5% 1% 4% 0% 10%
0-19 1% 0% 0% 4% 5%
Total 7% 15% 43% 35% 100%
Y: Time Studied
X: Scoreobtained
![Page 4: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/4.jpg)
Joint Probability Distributions
Joint Distribution
![Page 5: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/5.jpg)
Joint Probability Distributions
Example
![Page 6: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/6.jpg)
Joint Probability Distributions
Example
![Page 7: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/7.jpg)
Joint Probability Distributions
Marginal Distribution
![Page 8: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/8.jpg)
Joint Probability Distributions
Independent Random Variables
![Page 9: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/9.jpg)
Joint Probability Distributions
Expected Values
![Page 10: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/10.jpg)
Joint Probability Distributions
Covariance
![Page 11: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/11.jpg)
Joint Probability Distributions
Correlation
![Page 12: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/12.jpg)
Joint Probability Distribution
Distribution of the Sampling Mean
![Page 13: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/13.jpg)
Joint Probability Distributions
Example 5.24 (1/2): Sampling mean Distribution
![Page 14: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/14.jpg)
Joint Probability Distributions
Example 5.24 (2/2): Sampling mean Distribution
![Page 15: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/15.jpg)
Joint Probability Distributions
Distribution of the Sampling Mean
![Page 16: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/16.jpg)
Joint Probability Distributions
Distribution of the Sampling Mean
![Page 17: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/17.jpg)
Joint Probability Distributions
Central Limit Theorem (CLT)
![Page 18: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/18.jpg)
Joint Probability Distributions
Example: CLT
![Page 19: Probability and Statistics with Programminglecture.riazulislam.com/uploads/3/9/8/5/3985970/stat_8_sejong_2018_1.pdfProbability and Statistics with Programming Course Code 009959 (Spring](https://reader034.vdocument.in/reader034/viewer/2022050716/5e23637e5c0c4f2ea33ee648/html5/thumbnails/19.jpg)
Q&A