Basic probability & statistics
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Transcript of Basic probability & statistics
Basic Probability and Statistic
Editor: Nguyen Duc Minh KhoiEmail: [email protected]
Website: https://nguyenducminhkhoi.blogspot.com
Probability: The basics
Probability: The basics (cont.)• Conditional Probability
• Independence
Probability: The basics (cont.)• Rule of total Probability:
• Bayes Rule:
• Chain rule
iiBAPBPAp |
)(
)|()(|
yP
xyPxPyxP
Probability: Random Variable (rv) – PMF vs. PDF• Discrete RV
• Continuous RV
Probability: Random Variable (rv) - Cumulative Density Functions (CDF)
Probability: Expectations
Probability: Expectations (cont.)
• Conditional expectation
Probability: Expectations (cont.)
• Other important Values
• Example:
Probability: Important discrete rv
Probability: Important continuous rv
Probability: Multiple variables
Probability: Multiple variables (Covariance & Correlation)
Law of large number & Central Limit Theorem
Statistics• Give data, how to find the model (pattern) of this
data.
• 2 school of thoughts:
• 𝜃in Bayesian is a rv (have prior p(𝜃)); 𝜃 in Classical is unknown constant.
Classical Inference: Maximum Likelihood Estimator (MLE)
Step: 1. Log; 2. derive; 3. solve for 𝜃
Classical Inference: Other methods• Linear Regression
Bayesian Inference:
Bayesian Inference (cont.)
References
• http://www.stanford.edu/class/cme308/OldWebsite/notes/chap2.pdf
• http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/resource-index/
• Bertsekas, Dimitri P. Introduction to Probability: Dimitri P. Bertsekas and John N. Tsitsiklis. Athena scientific, 2002.