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StatisticsExamTopics - Probability and Statistics I(MAT651...

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Probability and Statistics I (MAT651) 1. Axiomatic Foundations, The Calculus of Probabilities, Counting, Enumerating Outcomes. Conditional Probability and Independence 2. Random Variables, Distribution Functions, Density and Mass Functions 3. Distributions of Functions of a Random Variable 4. Moments and Moment Generating Functions, Characteristic Functions 5. Common Families of Distributions: Binomial, Hypergeometric, Geometric, Poisson, Negative Binomial, Uniform, Exponential, Normal, Gamma, Beta. 6. Multiple Random Variables: Joint and Marginal Distributions, Conditional Distributions and Independence, Bivariate Transformations, Multivariate Distributions 7. Random Samples: Sum of Random Variables from a Random Sample, Sample Mean. 8. Sampling From a Normal Sample. 9. Order Statistics 10. Convergence Concepts: Convergence in Probability, Convergence in Distribution, Delta Method. Probability and Statistics II (MAT652) 1. Principles of Data Reduction: Sufficiency Principle, Likelihood Principle, Equivariance Principle 2.
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