#### List of posts on Algebra, Statistics, Econometrics, Finance and Optimization.

My feeling is that this site map is not very useful. If you have suggestions how it can be improved, drop me an email.

#### See My credo and How to save on my book

## Pages

- About the author
- About the book
- Basic statistics
- Book reviews
- Donor Dashboard
- Econometrics
- Matrix algebra
- Optimization
- Quant Finance
- Search Results
- Site map
- Advanced Statistics
- Useful links

## Posts by category

**Category: Advanced Statistics ST2133**- 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
- The pearls of AP Statistics 36
- Statistical measures and their geometric roots
- Properties of standard deviation
- The pearls of AP Statistics 35
- The pearls of AP Statistics 34
- Properties of variance
- The pearls of AP Statistics 33
- Properties of means
- The pearls of AP Statistics 32
- The pearls of AP Statistics 31
- The pearls of AP Statistics 30
- The pearls of AP Statistics 29
- The pearls of AP Statistics 28
- The pearls of AP Statistics 27
- The pearls of AP Statistics 26
- The pearls of AP Statistics 25
- The pearls of AP Statistics 24
- The pearls of AP Statistics 23
- The pearls of AP Statistics 22
- The pearls of AP Statistics 21
- The pearls of AP Statistics 20
- The pearls of AP Statistics 19
- The pearls of AP Statistics 18
- The pearls of AP Statistics 17
- The pearls of AP Statistics 16
- The pearls of AP Statistics 15
- The pearls of AP Statistics 14
- The pearls of AP Statistics 12
- The pearls of AP Statistics 11
- The pearls of AP Statistics 10
- The pearls of AP Statistics 9
- The pearls of AP Statistics 8
- The pearls of AP Statistics 7
- The pearls of AP Statistics 6
- The pearls of AP Statistics 5
- The pearls of AP Statistics 4
- The pearls of AP Statistics 3
- The pearls of AP Statistics 2
- The pearls of AP Statistics 1
- Properties of conditional expectation
- What is a p value?

**Category: Agresti and Franklin****Category: AP Stats and Business Stats**- 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
- Intro to option greeks: delta and its determinants
- Interest rate - the puppetmaster behind option prices
- How to study mt3042 Optimisation: a guide to a guide
- 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
- The pearls of AP Statistics 37
- 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
- How to save on my book
- 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
- First message

**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**- 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
- See if this definition of a function is better than others
- Logical structure of definitions
- Solution to exercise 6.1: how to use homogeneity
- The right solution to Example 6.5
- 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**