機率與統計

此課程為AI聯盟之課程,對應人工智慧探索應用學分學程(機率)。 1. Experiments, Models, and Probabilities 1) Applying Set Theory to Probability 2) Conditional Probability 3) Independence 2. Basics of Random Variables 1) Definitions 2) Probability Mass Function (PMF) 3) Families of Discrete Random Variables 4) Cumulative Distribution Function (CDF) 5) Probability Density Function (PDF) 6) Families of Continuous Random Variables 3. Random Variables and Expected Value 1) Conditional Probability Mass/Density Function 2) Probability Models of Derived Random Variables 3) Variance and Standard Deviation 4) Expected Value of a Derived Random Variable 4. Multiple Random Variables 1) Joint Cumulative Distribution Function 2) Joint Probability Mass/Density Function 3) Marginal PMF/PDF 4) Functions of Two Random Variables 5) Conditioning by a Random Variable 6) Independent Random Variables 5. Sums of Random Variables 1) Expected Values of Sums 2) PDF of the Sum of Two Random Variables 3) Moment Generating Functions 4) MGF of the Sum of Independent Random Variables 5) Random Sums of Independent Random Variables 6) Central Limit Theorem 7) Law of Large Numbers

課堂參與及作業(50%)、期中課程評量成績(25%)、期末課程評量成績(25%)

Probability and Stochastic Processes - A Friendly Introduction for Electrical and Computer Engineers," Second Edition