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Week - 1 |
Sample Space and Probability: Introduction to probability theory, Review of set theory, Probability spaces, Axioms and properties of probability |
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Week - 2 |
Discrete and continuous probability laws, Conditional probability |
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Week - 3 |
Law of total probability and Bayes’ theorem, Independence and conditional independence, Independent trials and counting techniques |
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Week - 4 |
Discrete Random Variables: Introduction and examples of probability mass functions (PMFs), Expectation, mean, and variance |
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Week - 5 |
Properties of expectation and variance, Joint PMFs, Conditional PMFs, |
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Week - 6 |
Conditioning one random variable on another, Conditional expectation, Iterated expectation |
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Week - 7 |
Independence of a random variable from an event, Independence of random variables; General Random Variables: Continuous random variables and probability density functions (PDFs) |
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Week - 8 |
Expectation and the cumulative distribution function (CDF), The Gaussian CDF, Conditional PDFs and joint PDFs, Conditioning one random variable on another, |
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Week - 9 |
Independence and the continuous Bayes’ rule |
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Week - 10 |
Advanced Topics on Random Variables: Derived distributions, Functions of two random variables, |
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Week - 11 |
Correlation and covariance, Applications of covariance; |
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Week - 12 |
Conditional expectation and variance |
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Week - 13 |
EN: EN: Transforms (Moment Generating Functions), Introduction to statistics, Data Representation, Random Sampling, Point Estimation of Parameters |
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Week - 14 |
EN: EN: Confidence Intervals, Testing of Hypotheses (Decisions), Goodness of Fit, Nonparametric Tests, Regression, Fitting Straight Lines |
Eskisehir Technical University Info Package