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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The slowest run vs. the fastest walk: which is faster?
Suppose there are twins with exactly same physical strength. One of them runs as slowly as he/she can, and the other walks as fast as one can. Who would be the one that crosses the finish line first?
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Application of Dynkin's π-λ theorem
When dealing with collections of sets, Dynkin’s systems provides simple but powerful tool for extension of properties in smaller collections to bigger ones.
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Kolmogorov's maximal inequality with shifted starting point
Kolmogorov’s maximal inequality provides result similar to that of Chebyshev’s inequality to maximum of partial sum of random variables.
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