• Kairat Mynbaev wrote a new post 3 months ago

Simple tools for combinatorial problemsSolution to problem 1(b) from exam ST2133 ZA, 2019 Simple tools for combinatorial problems Before solving the problem, it is useful to compare the case […]

• The magic of the distribution functionThe magic of the distribution function Let \$latex X\$ be a random variable. The function \$latex F_{X}left( xright) =Pleft( Xleq xright) ,\$ where […]

• Final exam in Advanced Statistics ST2133, 2022

Unlike most UoL exams, here I tried to relate the theory to practical issues.

KBTU International School of Economics

Compiled by Kairat Mynbaev

The total for this […]

• A problem to do once and never come back

There is a problem I gave on the midterm that does not require much imagination. Just know the definitions and do the technical work, so I was hoping we could put this […]

• Marginal probabilities and densities

This is to help everybody, from those who study Basic Statistics up to Advanced Statistics ST2133.

Discrete case

Suppose in a box we have coins and banknotes of only two […]

• Strategies for the crashing market

This year is a wonderful time to short the market. During the pandemic the Fed has been pumping money into the market, and it was clear that the huge rally from March 2020 to […]

• This post is not an obituary. This is an ode to a living Teacher.

Early years

Mukhtarbai Otelbaev (I will call him MO for short) surprised us at the first meeting. It was a time when we had more strength than […]

• Vector autoregression (VAR)

Suppose we are observing two stocks and their respective returns are \$latex x_{t},y_{t}.\$ To take into account their interdependence, we consider a vector autoregression

(1) \$latex […]

• Vector autoregressions: preliminaries

Suppose we are observing two stocks and their respective returns are \$latex x_{t},y_{t}.\$ A vector autoregression for the pair \$latex x_{t},y_{t}\$ is one way to take into […]

• Blueprint for exam versions

This is the exam I administered in my class in Spring 2022. By replacing the Poisson distribution with other random variables the UoL examiners can obtain a large variety of versions […]

• Kairat Mynbaev wrote a new post 2 years ago

Estimation of parameters of a normal distribution

Here we show that the knowledge of the distribution of \$latex s^{2}\$ for linear regression allows one to do without long calculations contained in the guide ST […]

• Kairat Mynbaev wrote a new post 2 years ago

Distribution of the estimator of the error variance

If you are reading the book by Dougherty: this post is about the distribution of the estimator  \$latex s^2\$ defined in Chapter 3.

Consider regression

(1) […]

• Kairat Mynbaev wrote a new post 2 years ago

Sufficiency and minimal sufficiency

Sufficient statistic

I find that in the notation of a statistic it is better to reflect the dependence on the argument. So I write for a statistic, where is a sample, […]

• Chi-squared distribution Chi-squared distribution This post is intended to close a gap in J. Abdey’s guide ST2133, which is absence of distributions widely used in […]

• Gamma distributionGamma distribution Definition. The gamma distribution is a two-parametric family of densities. For the density is defined by  (replace […]

• Gamma functionGamma function The gamma function and gamma distribution are two different things. This post is about the former and is a preparatory step to study the […]

• Analysis of problems with conditioningAnalysis of problems with conditioning These problems are among the most difficult. It’s important to work out a general approach to such problems. All […]

• Sum of random variables and convolution Sum of random variables and convolution Link between double and iterated integrals Why do we need this link? For simplicity consider the rectangle The […]

• Leibniz integral rule Leibniz integral rule This rule is about differentiating an integral that has a parameter in three places: the lower and upper limits of integration and […]

• Solution to Question 1 from UoL exam 2020

The assessment was an open-book take-home online assessment with a 24-hour window. No attempt was made to prevent cheating, except a warning, which was pretty realistic. […]