Probability and Statistics with...

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: riaz@sejong.ac.kr

Probability Distributions in R

Concepts of Joint Probability Distributions

Expected Values, Covariance, and Correlation

Central Limit Theory

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

Joint Probability Distributions

Joint Distribution

Joint Probability Distributions

Example

Joint Probability Distributions

Example

Joint Probability Distributions

Marginal Distribution

Joint Probability Distributions

Independent Random Variables

Joint Probability Distributions

Expected Values

Joint Probability Distributions

Covariance

Joint Probability Distributions

Correlation

Joint Probability Distribution

Distribution of the Sampling Mean

Joint Probability Distributions

Example 5.24 (1/2): Sampling mean Distribution

Joint Probability Distributions

Example 5.24 (2/2): Sampling mean Distribution

Joint Probability Distributions

Distribution of the Sampling Mean

Joint Probability Distributions

Distribution of the Sampling Mean

Joint Probability Distributions

Central Limit Theorem (CLT)

Joint Probability Distributions

Example: CLT

Q&A