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,

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