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Week - 1 |
Fundamentals of Probability Theory: Sample Space, Events, Combinatorial Analysis and Counting Techniques (Permutation, Combination) |
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Week - 2 |
Axioms of Probability: Definition of Probability, Venn Diagrams, Set Operations and Probability Rules |
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Week - 3 |
Conditional Probability and Independence: Definition of Conditional Probability, Multiplication Rule, Theorem of Total Probability and Independent Events |
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Week - 4 |
Bayes' Theorem: Bayes' Rule, Medical Testing/Error Analysis Examples and Introduction to AI Applications |
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Week - 5 |
Random Variables I: Discrete Random Variables, Probability Mass Function (PMF) and Cumulative Distribution Function (CDF) |
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Week - 6 |
Discrete Probability Distributions: Bernoulli, Binomial, Geometric and Poisson Distributions with Applications |
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Week - 7 |
Random Variables II: Continuous Random Variables, Probability Density Function (PDF) and Continuous CDF |
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Week - 8 |
Continuous Probability Distributions: Uniform, Exponential and Normal (Gaussian) Distribution |
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Week - 9 |
Expected Value and Variance: Expected Value, Variance, Standard Deviation of Random Variables and Moments |
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Week - 10 |
Multivariate Distributions I: Joint Probability Distributions, Discrete and Continuous Joint PDF/PMF Structures |
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Week - 11 |
Multivariate Distributions II: Marginal and Conditional Distributions, Independent Random Variables |
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Week - 12 |
Associations and Matrices: Concept of Covariance, Correlation Coefficient, Covariance and Correlation Matrices |
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Week - 13 |
Limit Theorems: Chebyshev's Inequality, Law of Large Numbers (Weak and Strong) and Central Limit Theorem (CLT) |
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Week - 14 |
Introduction to Stochastic Processes: Concept of Random Processes, Markov Chains, State Transition Matrices and Diagrams |