# Tagged Questions

Use this tag only if your question is about the modern theoretical footing for probability, for example probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for specific problems and explicit computations. Use [tag:probability-...

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### Find variance of happy people sitting at $n$ regular polygon table

Let table has shape of $n$ regular polygon and at each side is sitting one person. Each person is flipping a fair coin once (results of $n$ independent tosses are independent). Person is happy iff he ...
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### Random walk on d-dimensional torus

I am reading the following paper: http://arxiv.org/pdf/1602.03849v2.pdf I will explain the general setup below. Let $x\in X=\mathbb{T}^d$, where $\mathbb{T}^d$ is the d dimensional torus. Let $\rho$ ...
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### CGF determines the distribution

It is well known, that if the domain of the mgf of a random variable $X$ contains an interval around zero, then the distribution is completely determined by its moments. However consider a Levy-...
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### Probability question, can I reset the window or not

There is a wall street banker. The banker invests in a kind of share called as options. The main features of this share is as follows: You make a bet with a specified amount of information as to ...
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### Sequence of Erdos-Renyi random graphs convergent with probability 1

Definitions Let $H,G$ be finite simple graphs. Then the density of $H$ in $G$, denoted $d(H,G)$, is defined as the probability that a randomly chosen $|H|$-tuple of vertices of $G$ induce a graph ...
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### How does commutative property play a big role in probability theory? Kindly, explain why do we need free-independence?

I got to know that as matrix operations are non-commutative, calculation of moments are not possible? To be able to do so, one need to ralax the independence to something called free-independence. I ...
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### probability of having an ace on each hand when dealing 52 cards to 4 hands

The question from DeGroot's book: "probability and statistics" "Suppose that a deck of 52 cards containing four aces is shuffled thoroughly and the cards are then distributed among four players so ...
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### What is Steiltjes transform (other Integral transform) and how does it helps in probability theory, specifically in random matrix theory?

I have started growing interest in random matrix theory. Trying to understand it from "Random Matrices" by Madan Lal Mehta and "An Introduction to Random Matrices" by Anderson and many sources on ...
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### Help understanding convolutions for probability?

I have been trying to do some problems in probability that use convolutions but there has not been much of an explanation of what a convolution is or the purpose of using a convolution. For example ...
### Given $n$ heads out of $n$ tosses. What is the posterior probability that coin is fair? [closed]
I am given an $\sigma$-fair coin with the probability of head $(\theta)$ being in the interval $[\frac{1}{2} - \sigma, \frac{1}{2} + \sigma]$. Also I am given: For a Bayesian analysis of the ...