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- Category: Abstract Math
- Category: Advanced Statistics ST2133
- Unit 5.8. Standard deviation
- Unit 5.7. Variance
- Unit 5.6. Covariance
- Unit 5.5. Independence and its consequences
- Unit 5.4. Linearity
- Unit 5.3. Linear combinations of random variables
- Unit 5.2. General properties of means
- Unit 5.1. Random variable
- Unit 4.10. Questions for repetition
- Unit 4.9. Problem solving strategy
- Unit 4.8. Conditional probabilities
- Unit 4.7. All about joint events
- Unit 4.6. Combinatorics
- Unit 4.5. Ways to find probabilities
- Unit 4.4. Probability
- Unit 4.3. Set versus probabilistic terminology
- Unit 4.2. Set identities
- Unit 4.1. Set operations
- Unit 3.6. Questions for repetition
- Unit 3.5. Measures of relationships
- Unit 3.4. Measures of variability
- Unit 3.3. Shape of the distribution
- Unit 3.2. Measures of central tendency
- Unit 3.1. Three representations of data: raw, ordered and frequency
- Unit 2.4. Questions for repetition
- Unit 2.3. Visualizing statistical data
- Unit 2.2. Frequencies and distributions
- Unit 2.1. Classification of variables
- Units 1.3 and 1.4. Ways to think about things, and questions for repetition
- Unit 1.2. Studying a definition
- Simple tools for combinatorial problems
- The magic of the distribution function
- Final exam in Advanced Statistics ST2133, 2022
- A problem to do once and never come back
- Marginal probabilities and densities
- Midterm Spring 2022
- Estimation of parameters of a normal distribution
- Sufficiency and minimal sufficiency
- Chi-squared distribution
- Gamma distribution
- Gamma function
- Sum of random variables and convolution
- Leibniz integral rule
- Category: Advanced Statistics ST2134
- Category: Agresti & Franklin
- Conditional variance properties
- Multiple regression through the prism of dummy variables
- Testing for structural changes: a topic suitable for AP Stats
- It’s time to modernize the AP Stats curriculum
- Ditch statistical tables if you have a computer
- Nonparametric estimation for AP Stats
- Properties of correlation
- Statistical measures and their geometric roots
- Properties of standard deviation
- Properties of variance
- Properties of means
- Properties of conditional expectation
- What is a p value?
- Category: Agresti and Franklin
- Category: AP Stats and Business Stats
- Unit 14.2. Excel functions for critical values
- Unit 14.1. Excel functions for distributions
- Unit 13.6. Questions for repetition
- Unit 13.5. Criterion of linear dependence and the dummy variable trap
- Unit 13.4. Linear dependence of vectors
- Unit 13.3. Model with two regressors
- Unit 13.2. How to read Dougherty's book
- Unit 13.1. Problems with LSE econometrics
- Unit 12.4. Two-way ANOVA: decompositions and F-tests
- Unit 12.3. Two-way ANOVA: setup and population model
- Unit 12.2. One-way ANOVA: distributions and the F-test
- Unit 12.1. One-way ANOVA: setup and the SST decomposition
- Unit 11.4. Questions for repetition
- Unit 11.3. Application to the linear model
- Unit 11.2. Exponential and Bernoulli distributions
- Unit 11.1. Main idea and algorithm
- Unit 10.6. Questions for repetition
- Unit 10.5. Goodness of fit
- Unit 10.4. Orthogonality and its consequences
- Unit 10.3.5. Statistics for testing hypotheses
- Unit 10.3.4. Variances of OLS estimators
- Unit 10.3. Unbiasedness of OLS estimators
- Unit 10.3. Ordinary Least Squares (OLS): definition and derivation
- Unit 10.2. Linear model setup
- Unit 10.1. Algebra of sample means
- Unit 9.7. Questions for repetition
- Unit 9.6. Testing for equality of two sample variances
- Unit 9.5. Power of a test
- Unit 9.4. p-values
- Unit 9.3. Confidence intervals and hypothesis testing
- Unit 9.2. Tradeoff between Type I and Type II errors
- Unit 9.1. Concepts of hypothesis testing
- Unit 8.5. Questions for repetition
- Unit 8.4.5. Difference between two population proportions
- Unit 8.4.4. Independent samples. Case III (Satterthwaite's formula)
- Unit 8.4.3. Independent samples. Case II
- Unit 8.4.2. Independent samples. Case I
- Unit 8.4.1. Matched pairs
- Unit 8.3.3. Confidence interval for population proportion
- Unit 8.3.2. Confidence interval for the population mean. Case of an unknown variance
- Unit 8.3.1. Confidence interval for the population mean. Case of a known variance
- Unit 8.2. Consistency
- Unit 8.1. Unbiasedness and efficiency
- Unit 7.4. Questions for repetition
- Unit 7.3. Monte Carlo simulations
- Unit 7.2. Sampling distribution of sample variance
- Unit 7.1. Sampling distribution
- Unit 6.10. Questions for repetition
- Unit 6.9. Exponential distribution and link to Poisson
- Unit 6.8. Joint distribution and independence
- Unit 6.7. Normal approximation to the binomial
- Unit 6.6. The normal distribution
- Unit 6.5. The uniform distribution
- Unit 6.4. Mean, covariance, variance and correlation
- Unit 6.3. Mean value of a continuous random variable
- Unit 6.2. Density
- Unit 6.1. Properties of integrals
- Unit 5.18. Questions for repetition
- Unit 5.17. Portfolio analysis
- Unit 5.16. Poisson approximation to the binomial
- Unit 5.15. Poisson distribution
- Unit 5.14. Distribution function
- Unit 5.13. Distribution of the binomial variable
- Unit 5.12. An obvious and handy result
- Unit 5.11. Bernoulli variable
- Unit 5.10. Standardization
- Unit 5.9. Correlation coefficient
- Unit 12.5. Questions for repetition
- Unit 1.1. The structure of mathematics
- Units 1.1-1.2. The structure of mathematics
- Early Education and Brainbuilding
- AR(1) model: Tesla stock versus Tesla return
- Analysis of problems with conditioning
- My book is gaining international recognition
- My book in Basic Statistics
- Statistical calculator
- My book milestone
- Music for work and pleasure
- A singer you shouldn't miss
- AP Statistics the Genghis Khan way 2
- AP Statistics the Genghis Khan way 1
- Little tricks for AP Statistics
- Law of total probability - you could have invented this
- Distribution function estimation
- See if this definition of a function is better than others
- Intro to option greeks: delta and its determinants
- Interest rate - the puppetmaster behind option prices
- Finite Horizon Dynamic Programming
- Reevaluating probabilities based on piece of evidence
- Significance level and power of test
- Violations of classical assumptions 2
- Alternatives to simple regression in Stata
- Running simple regression in Stata
- Examples of distribution functions
- Density function properties
- Gauss-Markov theorem
- Regressions with stochastic regressors 2
- The law of large numbers proved
- Inductive introduction to Chebyshev inequality
- Regressions with stochastic regressors 1
- OLS estimator variance
- Properties of covariance
- All you need to know about the law of large numbers
- Proving unbiasedness of OLS estimators
- Derivation of OLS estimators: the do's and don'ts
- What is cointegration?
- What is a mean value - all means in one place
- Summation sign rules: identities for simple regression
- Simple regression - before and after estimation
- OLS estimator for multiple regression - simplified derivation
- Teaching methodology dilemma: Is lecturing good or bad?
- What is an OLS estimator - simplified derivation
- What is a binomial random variable - analogy with market demand
- What is a z score: the scientific explanation
- Scaling a distribution
- Mean plus deviation-from-mean decomposition
- Active learning - away from boredom of lectures
- Population mean versus sample mean
- Modeling a pair of random variables and scatterplot definition - Exercise 2.5
- Histogram versus time series plot - Example 2.2
- Modeling a sample from a normal distribution in Excel - Exercise 2.4
- Creating frequency table and histogram and using Excel macros - Exercise 2.3
- Simulating the binomial variable - Exercise 2.2
- Generating Bernoulli random variable (coin) in Excel - Exercise 2.1
- Category: Book reviews
- Category: Dimash Kudaibergen
- Category: Dougherty Introduction to Econometrics
- Distributions derived from normal variables
- Application: Ordinary Least Squares estimator
- Violations of classical assumptions 1
- Nonlinear least squares: idea, geometry and implementation in Stata
- Introduction to Stata
- Autoregressive–moving-average (ARMA) models
- Moving average processes
- Autoregressive processes
- Stationary processes 2
- Stationary processes 1
- Nonstationary processes 2
- Error correction model
- Maximum likelihood: application to linear model
- Distribution and density functions of a linear transformation
- Maximum likelihood: idea and life of a bulb
- Binary choice models: theoretical obstacles
- Binary choice models
- Distribution function properties
- Durbin-Wu-Hausman test
- Instrumental variables estimator
- What is a stationary process?
- Category: EC2020
- Category: EC2020 Elements of econometrics
- Category: Econometrics
- Category: FN3142 Quantitative Finance
- Conditional expectation as a projector
- Optimal forecast properties
- Strategies for the crashing market
- Vector autoregression (VAR)
- Vector autoregressions: preliminaries
- Solution to Question 1 from UoL exam 2020
- Put debit spread
- Call debit spread
- Solution to Question 2 from UoL exam 2018, Zone B
- Solution to Question 2 from UoL exam 2019, zone B
- Solution to Question 3 from UoL exam 2019, zone A
- FN3142 Chapter 14 Risk management and Value-at-Risk: Backtesting
- FN3142 Chapter 13. Risk management and Value-at-Risk: Models
- FN3142 Chapter 12. Forecast comparison and combining
- Leverage effect: the right definition and explanation
- Question 1 from UoL exam 2016, Zone B, Post 2
- Question 1 from UoL exam 2016, Zone B, Post 1
- Solution to Question 3b) from UoL exam 2018, Zone A
- Checklist for Quantitative Finance FN3142
- Law of iterated expectations: geometric aspect
- Law of iterated expectations: informational aspect
- Portfolio analysis: return on portfolio
- Applications of the diagonal representation IV
- Efficient market hypothesis is subject to interpretation
- The Newey-West estimator: uncorrelated and correlated data
- Solution to Question 2 from UoL exam 2016, zone A
- Sampling from uniform distribution - example of convolution
- Density of a sum of independent variables is given by convolution
- Solution to Question 1 from UoL exam 2017, Zone B
- Solution to Question 1 from UoL exam 2016, Zone B
- Solution to Question 1 from UoL exam 2016, Zone A
- Expected shortfall is next after Value at Risk
- Conditional expectation generalized to continuous random variables
- Value at Risk and its calculation for a normal distribution
- Visualization of payoffs on calls and puts
- Intro to option greeks: theta, intrinsic value and time value
- Option chain and efficient market hypothesis
- Volatility - king among option price determinants
- Call options and probabilistic intuition - dependence on time
- Call options and probabilistic intuition - dependence on stock price
- Call options and probabilistic intuition - dependence on strike
- Old versus new tools in Quantitative Finance
- Canonical form for time series
- Conditional-mean-plus-remainder representation
- Category: Matrix algebra
- Sylvester's criterion
- Gaussian elimination method
- Elementary transformations
- Main theorem: Jordan normal form
- Playing with bases
- Chipping off root subspaces
- Action of a matrix in its root subspace
- Properties of root subspaces
- Direct sums of subspaces
- Correctness of the space dimension definition
- Determinants: questions for repetition
- Laplace expansion
- Cramer's rule and invertibility criterion
- Determinant of a transpose
- Multilinearity in columns
- Determinant of a product
- Leibniz formula for determinants
- Properties of permutation matrices
- Permutation matrices
- Properties IV-VI
- Axioms 1-3 and Properties I-III
- Determinants: starting simple
- Questions for repetition
- Eigenvalues and eigenvectors of a projector
- Constructing a projector onto a given subspace
- Geometry and algebra of projectors
- Questions for repetition
- Questions for repetition
- Applications of the diagonal representation III
- Applications of the diagonal representation II
- Applications of the diagonal representation I
- Diagonalization of symmetric matrices
- General properties of symmetric matrices
- Eigenvalues and eigenvectors
- Orthogonal matrices
- Matrix similarity
- Final touches on linear independence
- Law and order in the set of matrices
- Complex numbers: time to turn on the beacon
- Summary and questions for repetition
- Rank of a matrix and the rank-nullity theorem
- Basis and dimension
- Linear dependence of vectors: definition and principal result
- Solvability of an equation with a square matrix
- Is the inverse of a linear mapping linear?
- Geometry of linear equations: questions for repetition
- Geometry of linear equations: orthogonal complement and equation solvability
- Geometry of linear equations: structure of image and null space
- Geometry of linear equations: linear spaces and subspaces
- Geometry of linear equations: matrix as a mapping
- Euclidean space geometry: questions for repetition
- Euclidean space geometry: Cauchy-Schwarz inequality
- Euclidean space geometry: scalar product, norm and distance
- Euclidean space geometry: vector operations
- Matrix algebra: questions for repetition
- Matrix transposition: continuing learning by doing
- From invertibility to determinants: argument is more important than result
- Matrix inversion: doing some housekeeping at elementary level
- Roadmap for studying matrix multiplication
- Vector and matrix multiplication
- Matrix notation and summation
- Category: MT2175 Further linear algebra
- Category: MT3042 Optimisation theory
- From minimum to infimum: Math is just a logical game
- Logical structure of definitions
- Solution to exercise 6.1: how to use homogeneity
- The right solution to Example 6.5
- How to study mt3042 Optimisation: a guide to a guide
- The economical way to use the Kuhn-Tucker theorem
- Cauchy-Schwarz inequality and optimization 2
- Cauchy-Schwarz inequality and optimization 1
- Consumption-Savings Problem
- Using convexity in optimization
- The Kuhn-Tucker theorem ins and outs
- The Kuhn-Tucker theorem: a first look
- The Lagrangian multiplier interpretation
- Lagrange method: case of many equality constraints
- Lagrange method: sufficient conditions
- Lagrange method: necessary condition
- Importance of implicit function theorem for optimization
- Optimization with constraints: economic and financial examples
- Unconstrained optimization on the plane 2
- Unconstrained optimization on the plane 1
- Taylor decomposition for unconstrained optimization
- The Cobb-Douglas function and level sets
- Geometry behind optimization
- Geometry related to derivatives
- Category: Optimisation theory
- Category: Option properties
- Category: Quantitative Finance
- Category: ST104A
- Category: ST104B
- Category: Statistics 1
- Category: Statistics 2
- Category: The College Board
- Category: Uncategorized