# Tagged Questions

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### What background is required to understand Random Matrix Theory

I would like to be able to understand RMT but after "reading" many articles I have found that I have a limited capacity. I just see complicated equations. I guess I know linear algebra, classical ...
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### A measurement of “likelihood” of a roll of $n$ independent normal random variables

I'll start with a general question, and later, as I expect it is possible that the general case does not have a satisfying answer, I'll post my specific problem. I am trying to find some measurement ...
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### Examples for Conditional Expectation (modern probability theory)

I'm in the process of learning about conditional expectation in the framework of modern probability theory. The sudden change brought about by the notion of conditional expectation being a function on ...
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### Mathematics of a Simple Counting Game

I wonder how can one think mathematically about the following game: People sit in a circle. One of them says "One!". Then somebody (no matter who - he/she can even be the former person) says ...
340 views

### Real Analysis and Statistics

What level of real analysis do you think is desirable for the study of statistics? I know that for many statisticians with applied focus, rigorous mathematics tend to give them a headache and I am ...
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### Why do we want probabilities to be *countably* additive?

In probability theory, it is (as far as I am aware) universal to equate "probability" with a probabilistic measure in the sense of measure theory (possibly a particularly well behaved measure, but ...
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### Question on meaning probability of coin tosses?

I have a question on the fundamental meaning of probability. The most familiar example of probability, is the probability of $\frac 12$ for $\text{H}$ and $\text{T}$, each for a single toss of an ...
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### What is the relationship between variance and energy

I was speaking with someone today who told me that variance, in the sense of probability theory, is equivalent mathematically to energy in physics. Can anyone elaborate on this relationship?
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### Why are half-open intervals $(a,b]$ “special” in probability theory?

I'm learning probability theory and I see the half-open intervals $(a,b]$ appear many times. One of theorems about Borel $\sigma$-algebra is that The Borel $\sigma$-algebra of ${\mathbb R}$ is ...
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### Reference request for examples of probabilistic heuristics, help put some examples in a broader context.

I was thinking about how probability is used in heuristic arguments, an example being the argument that there are an infinite number of twin primes: the probability that $n$ is the first of two twin ...
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### What distinguishes the Measure Theory and Probability Theory?

It is clear that the Theory of Probability works primarily with limited measures on measurable spaces. On the other hand there is a folklore that says that what distinguishes the Theory of ...
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### Radical Applications of Algebraic Topology

Are there any radical applications of algebraic topology? For example, in probability theory we look at sample spaces. Suppose the sample space is a torus (for example). Would computing homology ...
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### Monty hosting a new show

I imagine the following setup. There is a contestant who has to pick one of three doors. How many prizes will be hidden is determined at random in the following way. Monty will toss a fair coin and ...
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### Sleeping Mathematician (Sleeping Beauty)

I came across the following thought experiment, and I would like to understand whether the controversy around it is justified. Imagine an experiment in which a mathematician is put to sleep with some ...
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### Chance of meeting in a bar

Two people have to spend exactly 15 consecutive minutes in a bar on a given day, between 12:00 and 13:00. Assuming uniform arrival times, what is the probability they will meet? I am mainly ...
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### Expository articles on Analysis and Probability theory

When I come across a notion from algebra or number theory which I don't know I usually check Keith Conrad's page to see if he has written something about it. Key features of his articles are a very ...
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### Relationship between Abstract Algebra and Probability Theory

Is there a relationship between abstract algebra and probability theory? I ask this because of the following laws: Axiom of Countable Additivity: If $A_1, A_2, \dots \in \mathcal{B}$ (where ...
Suppose we have some random variable $X$ that ranges over some sample space $S$. We also have two probability models $F$ and $G$. Let $f(x)$ and $g(x)$ be the probability density functions for these ...
### Uniform distribution on $\mathbb Z$ or $\mathbb R$
I was assisting once the course in Probability Theory where students learnt quite quickly that there are ways to assign the uniform distribution to any finite set - or even subsets of $\mathbb R$ of a ...