Resources
This space serves as a repository for reference materials, study notes, cheat sheets, and technical guides compiled throughout my studies and research.
Posts below are arranged chronologically—spanning probability theory, machine learning, software tools, and computational notes. You can also use the Archive to browse all articles organized by tags.
Selected notes have also been compiled into standalone PDF documents:
1.5. Convergence theorems and elementary inequalities
In the previous section, we defined the Lebesgue integral and the expectation of random variables and showed basic properties. However the additive property of integrals is yet to be proved. In addition, since our major interest throughout the textbook is convergence of random variables and its rate, we need our toolbox for it.
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1.4. The Lebesgue integral
In this section, we define the expectation of a random variable as the Lebesgue integral with respect to the probability measure. First, I will introduce the standard machine in measure theory and use it to define the Lebesgue integral. Next, the definition of expectation will be discussed in terms of the Lebesgue integral.
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1.3. Random variables
We take a closer look at random variables and random elements.
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1.2. Distributions
In this subsection, we define random variables and distribution functions.
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1.1. Basics on measure theory
The first year as an M.S. student in Statistics at SNU was the time spent for learning theoretical foundations of statistics. The probability theory was certainly the most emphasized subject of all. I would like to take this vacation as an opportunity to review the course on probability theory. Most of the content is from the book Probability: Theory and Examples, 5th edition (Durrett, 2019), while some others are borrowed from the lecture note and personal communications with colleagues.
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