# Tagged Questions

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### What is the best book to learn statistics?

Right now I'm taking a 3 part course on probability and statistics using Schverish & Degroot Probability and Statistics and it is just not helpful. For the first part, which was on Probability, I ...
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### References for a second course in probability theory

I need a probability book that treats all the arguments from the point of view of the measure theory and the Lebesgue integral. I've the basis of "naive" probability theory and of measure theory so I ...
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### Book on combinatorial identities

Do you know any good book that deals extensively with identities obtained using combinatorial and/or probabilistic arguments (e.g., by solving the same combinatorial or probability problem in two ...
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### Learning resources for Probability Distributions/Models

I've a good background in basic probability. I need to learn and get a good grip on the probability distributions and stochastic processes, counting processes, and other related topics. I am already ...
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### A list of different measures of distance/difference/dissimilarities/similarity of two probability distributions?

I wanted to know more about the different methods for comparing the similarities of two probability distributions P and Q. I wanted a list of the different methods that exist for comparing ...
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### Who discovered this number-guessing paradox?

In this math.se post I described in some detail a certain paradox, which I will summarize: $A$ writes two distinct numbers on slips of paper. $B$ selects one of the slips at random (equiprobably), ...
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### Introductory Statistics/Probability Reference Request

I am a PhD student in mathematics with a background in Pure Mathematics. As such I have pretty much zero background in statistics or anything other than the most basic probability (i.e., what one ...
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### Estimating the magnitude of a change in a non-stationary stochastic process

In this paper by Adams and MacKay, they present an algorithm for the online detection of change-points in a stochastic process subject to some hypotheses. Their algorithm gives both the predictive ...
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### References for problems related to uniformly distributed points/ arcs on circle

I am looking for references to problems related to computing the statistical properties of uniformly randomly chosen points or arcs on the unit circle, e.g.: On a unit circle, $n$ points are ...
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### The most fundamental papers in stochastic analysis

I have soft a question. What papers will be good to on start and allow me to make little step into research, without harm for reader. I am interested in an stochastic analysis. I am looking for ...
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### Expected state of a markov chain

Let's start with a slightly trivial Markov chain defined as follows: the beginning state is called $1$ and the set of states is $\mathbb{N}$. At each step, when the current state is $n$, the ...
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### Reference for the Law of the Unconscious Statistician?

Does anyone know of a reference (a book or journal article) for the Law of the Unconscious Statistician?
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### convergence to types theorem - reference

I'm looking for a good reference to the following (or similar) statement of the convergence to types theorem (good meaning a book or a research paper with a proof of this theorem) Let $X_n$ be a ...
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### Quickest path to proof of Central Limit Theorem?

I'm looking for a quick approach to a rigorous proof of the central limit theorem of probability theory. (I imagine that this would have to be a paper or monograph with this as its main goal, ...
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### Question about convergence in probability (topic confusion)

I'm taking second year stats and was introduced the below concepts For the third one, we use that to estimate the mean squared error in the case where the estimator is a nonlinear function of the ...
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### Conditions for the ground state of Gibbs ensemble not to be “degenerate”

I am looking at the Wikipedia article on Partition function -- As a measure. Unfortunately the article has no relevant references or reading suggestions. I am looking for books or other resources ...
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### Some long and good prerequisite textbooks to the graduate probability textbook by shiryaev and boas?

Some long and good prerequisite textbooks to the graduate probability textbook by shiryaev and boas? It seems that it have a big gap between this graduate textbooks and the easier ones.
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### literature to learn more on ergodic harris recurrent chains with an atom

I'm trying to learn more on the topic mentioned in the title. Namely I'd like to get more information on the behavior of the boundary terms. ie if I decompose sum of my chain (suppose it's ...
I'm trying to prove that if $X_i$ are independent, identically distributed random variables such that $E X_i = 0$ and $E X_i^2 < \infty$ then the sequence $\frac{(\sum_{i=1}^{n} X_i)^2}{n}$ is ...