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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]
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