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Probability theory. mathematical statistics and stochastic analysis

All lectures: All lectures on the discipline: probability theory. mathematical statistics and stochastic analysis are collected here. These fascinating lectures provide us with the opportunity to explore the deep principles and phenomena underlying our knowledge and our desire to understand the world.


1. Event. Random events. Event probability
2. Discrete random variables
3. Continuous random variables
4. Mathematical statistics
5. Laplace function and other tabular statistical functions: in Excel formula
6. Tables The value of the Laplace function f (x), tγ, q Critical points of the distribution of χ2 and Student
7. Expected value
8. Random Variance
9. Correlation
10. Regression analysis
11. Coefficient of determination
12. Linear regression
13. Least square method
14. Confidence interval
15. The confidence interval for the expectation of a normal sample
16. Confidence interval for normal sample variance
17. Normal distribution
18. Generating function
19. Generating function of moments
20. Generating function of a sequence (gentris)
21. Generating function of canonical transformation
22. Generatrix
23. Elementary event space
24. Numerical Characteristics of Random Variables
25. Poisson formula and an example of solving a problem
26. Bernoulli formula and an example problem solution
27. Bayes formula and examples of tasks
28. Full probability formula
29. The addition theorem for probabilities of incompatible events
30. Random events Event algebra Classical and statistical definitions of the probability of an event
31. the table of the main generating functions and the proof (conclusion).
32. Uniform distribution of random variable.
33. Geometric distribution
34. Binomial distribution
35. Poisson distribution
36. Standard normal distribution
37. Exponential distribution
38. . Multidimensional random variables. Random functions
39. Correlation coefficient properties
40. Distribution density of a system of two random variables
41. Polygon and histogram
42. Variance analysis
43. Random moments
44. Bertrand Paradox (probability)
45. Galton's board (quincunks) to demonstrate the central limit theorem
46. Probability
47. Probability distribution
48. Probability density
49. Quantile
50. Bayesian Spam Filtering
51. Rows of distribution. Polygon, Bar Graph, Cumulate, Ogiva
52. Summary and grouping of statistical data, Concept and types of grouping, Principles of grouping, Secondary grouping
53. Population and sampling method, Sampling errors, Sampling volume required
54. Types and analysis of time series. Methods for calculating the average level in the series of dynamics
55. Correlation and regression analysis. Linear correlation
56. Blind Signature Blind Signature
57. Random graph
58. 2.5. Almost impossible and almost reliable events. The principle of practical universality
59. 1.1. Subject of probability theory
60. 1.2. Brief historical information
61. 2.2. Direct calculation of probabilities
62. 2.3. Frequency, or statistical probability, of an event
63. 3.1. Purpose of the main theorems. Sum and Event
64. 3.2. Probability addition theorem
65. 3.3. Probability multiplication theorem
66. 3.4. Full probability formula
67. 3.5. Theorem of hypotheses (Bayes formula)
68. 4.1. Private theorem on repetition of experiments
69. 4.2. General repetition theorem
70. 5.1. A number of distribution. Polygon distribution
71. 5.2. Distribution function
72. 5.3. The probability of hitting a random variable on a given area
73. 5.4. Distribution density
74. 5.5. Numerical characteristics of random variables. Their role and purpose
75. 5.6. Position characteristics (expected value, mode, median)
76. 5.7. Moments. Dispersion. Standard deviation
77. 5.8. Uniform density law
78. 5.9. Poisson law
79. 6.1. Normal distribution law and its parameters
80. 6.2. Moments of normal distribution
81. 6.3. The probability of hitting a random variable in a given area. Normal distribution function
82. 6.4. Probable (median) deviation
83. 7.1. The main tasks of mathematical statistics
84. 7.2. Simple statistical aggregate. Statistical distribution function
85. 7.3. Statistical series. bar chart
86. 7.4 Numerical Characteristics of the Statistical Distribution
87. 7.5. Alignment of statistical series
88. 7.6. Consent Criteria
89. 8.1. The concept of a random variable system
90. 8.2. The distribution function of the system of two random variables
91. 8.3. Distribution density of a system of two random variables
92. 8.4. The laws of distribution of individual quantities included in the system. Conditional laws of distribution
93. 8.5 Dependent and independent random variables
94. 8.6. Numerical characteristics of a system of two random variables. Correlation moment. Correlation coefficient
95. 8.7. System of an arbitrary number of random variables
96. 8.8. Numerical characteristics of a system of several random variables
97. 9.1. Normal law on the plane
98. 9.2 Ellipses of dispersion. Reduction of the normal law to canonical form
99. 9.3. The probability of hitting a rectangle with sides parallel to the main axes of dispersion
100. 9.4. The probability of hitting an ellipse
101. 9.5. Probability of hitting an area of ​​arbitrary shape
102. 9.6. Normal law in the space of three dimensions.
103. 10.1. Expectation function. Function dispersion
104. 10.2. Numerical Characteristics Theorems
105. 10.3. Applications of theorems on numerical characteristics
106. 11.1. Method of linearization of functions of random arguments
107. 11.2. Linearize the function of one random argument
108. 11.3. Linearization of the function of several random arguments
109. 11.4. Refinement of the results obtained by the method of linearization
110. 12.1. The distribution law of the monotone function of one random argument
111. 12.2. The law of distribution of a linear function from an argument subject to the normal law
112. 12.3. The distribution law of a nonmonotonic function of one random argument
113. 12.4. The distribution law of the function of two random variables
114. 12.5. The distribution law of the sum of two random variables. The composition of the laws of distribution
115. 12.6. Composition of normal laws
116. 12.7. Linear functions of normally distributed arguments
117. 12.8. Composition of normal laws on the plane
118. 13.1. The law of large numbers and the central limit theorem
119. 13.2. Chebyshev Inequality
120. 13.3. The law of large numbers (Chebyshev theorem)
121. 13.4. The generalized Chebyshev theorem. Markov's theorem
122. 13.5. Consequences of the law of large numbers: theorems of Bernoulli and Poisson
123. 13.6. Mass random phenomena and the central limit theorem
124. 13.7. Characteristic functions
125. 13.8. Central limit theorem for equally distributed terms
126. 13.9. Formulas expressing the central limit theorem and occurring in its practical application
127. 14.1. Features of processing a limited number of experiments. Estimates of the length of the unknown parameters of the distribution law
128. 14.2. Estimates for expectation and variance
129. 14.3. Confidence interval Confidence probability
130. 14.4. Exact methods for constructing confidence intervals for random variable parameters
131. 14.5. Frequency probability estimate
132. 14.6. Estimates for the numerical characteristics of a system of random variables
133. 14.7. the task of processing the results of experimental firing (bombing).
134. 14.8. Smoothing of experimental dependencies by the least squares method
135. 15.1. Theory of random functions. Concept of random function
136. 15.2. The concept of a random function as an extension of the concept of a system of random variables. Distribution law of a random function
137. 15.3. Characteristics of random functions
138. 15.4. Characterization of a random function from experience
139. 15.5. Methods for determining the characteristics of the transformed random functions from the characteristics of the original random functions
140. 15.6. Linear and nonlinear operators. Dynamic system operator
141. 15.7. Linear transformations of random functions
142. 16.1. The idea of ​​the method of canonical decompositions. Representation of a random function as a sum of elementary random functions
143. 16.2. Canonical decomposition of a random function
144. 16.3. Linear transformations of random functions defined by canonical decompositions
145. 17.1. The concept of stationary random process
146. 17.2. Spectral decomposition of a stationary random function on a finite time interval. Dispersion spectrum
147. 17.3. Spectral decomposition of a stationary random function on an infinite segment of time. Spectral density of stationary random function
148. 17.4. Spectral decomposition of a random function in a complex form
149. 17.5. Transformation of stationary random function by stationary linear system
150. 17.6. Applications of the theory of stationary random processes to solving problems associated with the analysis and synthesis of dynamic systems
151. 17.7. Ergodic property of stationary random functions
152. 17.8. Characterization of an ergodic stationary random function in one implementation
153. The Simpson paradox in statistics with examples