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Week - 1 |
Introduction to probability theory: Sample space, concept of events, operations on events |
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Week - 2 |
Classical definition of probability, axiomatic approach to probability, probability measure and its fundamental properties |
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Week - 3 |
Conditional probability, independent events |
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Week - 4 |
Law of total probability, Bayes theorem |
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Week - 5 |
Concept of random variables, discrete and continuous random variables, distribution function |
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Week - 6 |
Probability mass function and probability density function |
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Week - 7 |
Expected value, variance |
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Week - 8 |
Higher moments, properties of the expected value |
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Week - 9 |
Discrete distributions: Bernoulli distribution, binomial distribution, geometric distribution, Poisson distribution |
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Week - 10 |
Continuous distributions: Uniform distribution, exponential distribution, normal distribution |
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Week - 11 |
Multivariate distributions: Joint distributions, marginal distributions |
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Week - 12 |
Conditional distributions, independence |
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Week - 13 |
Law of large numbers, central limit theorem |
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Week - 14 |
Random variable sequences and convergence concepts: Convergence in probability, almost sure convergence; Basic applications |