Probability Theory and Mathematical Statistics Course (MIPT FPMI)

[326/87%]

M. E. Zhukovskiy, I. V. Rodionov, D. A. Shabanov

Book 1Foundations of Probability Theory[114/83%]

Chapter 1.1Systems of Sets. Probability Space[9/78%]

Chapter 1.2Classical and Geometric Probabilities[9/67%]

Chapter 1.3Conditional Probability[7/57%]

Chapter 1.4The Concept of Independence. The Bernoulli Scheme[7/29%]

Chapter 1.5Probability Distributions[10/100%]

Chapter 1.6Random Variables[10/90%]

Chapter 1.7Independence, the Convolution Formula[12/83%]

Chapter 1.8Expectation in the Simplest Cases[8/100%]

Chapter 1.9Expectation (Other Cases), Covariance[8/88%]

Chapter 1.10Types of Convergence of Random Variables[7/100%]

Chapter 1.11Random Walk. The Borel–Cantelli Lemma[10/90%]

Chapter 1.12Characteristic Functions[10/100%]

Chapter 1.13Gaussian Vectors, the Central Limit Theorem[7/86%]

Book 2Introduction to Mathematical Statistics[112/88%]

Chapter 2.1Types of Convergence of Random Vectors[8/13%]

Chapter 2.2Statistics and Estimators[10/90%]

Chapter 2.3Methods for Finding Estimators[10/100%]

Chapter 2.4Comparison of Estimators and Efficient Estimators[9/78%]

Chapter 2.5Conditional Expectation[8/100%]

Chapter 2.6Conditional Distributions and Computing Conditional Expectations[8/100%]

Chapter 2.7Sufficient Statistics and Optimal Estimators[8/100%]

Chapter 2.8Confidence Intervals[8/100%]

Chapter 2.9Linear Regression[7/100%]

Chapter 2.10Testing Statistical Hypotheses[8/75%]

Chapter 2.11Testing Linear Hypotheses in the Gaussian Regression Model[6/100%]

Chapter 2.12Goodness-of-Fit Tests[8/100%]

Chapter 2.13Correlation Coefficients[8/88%]

Chapter 2.14Bayesian Estimators[6/100%]

Book 3Foundations of the Theory of Stochastic Processes[100/88%]

Chapter 3.1Basic Concepts of the Theory of Stochastic Processes[7/57%]

Chapter 3.2Galton-Watson Branching Processes[8/88%]

Chapter 3.3Processes with Independent Increments. The Poisson Process[8/75%]

Chapter 3.4Gaussian Processes. The Wiener Process[9/89%]

Chapter 3.5Markov Times[9/78%]

Chapter 3.6Martingales[8/88%]

Chapter 3.7Markov Processes[7/100%]

Chapter 3.8Discrete-Time Markov Chains[7/100%]

Chapter 3.9Continuous-Time Markov Chains[7/100%]

Chapter 3.10Linear Transformations in the Space

L^2

[7/86%]

Chapter 3.11Stationary Stochastic Processes[7/100%]

Chapter 3.12Spectral Representation[8/100%]

Chapter 3.13Elements of Itô Stochastic Calculus[8/88%]