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Questions tagged [probability]

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27 views

Usage of terms prior and posterior in probability

Probability function is of two types in general. They are unconditional probability and conditional probability. But the terms prior probability and posterior probability are used in place of ...
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0answers
26 views

Introduction of shape parameters in the formulation of probability distribution

I'm familiar with the definition of location, scale, and shape parameters, and the type of distributions they parametrized. I'm interested in understanding how shape parameters became part of the ...
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1answer
91 views

What is Peirce doing in this pre-Chi-squared example?

In 1878, C. S. Peirce performed a calculation that (I think) would be better done using chi-squared testing — but Pearson hasn’t introduced that yet. What exactly is Peirce doing here in the last ...
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2answers
237 views

Who coined the term “uniform” as in “uniform distribution”?

During the late 16th century and early 17th century, published work about probability theory (e.g. Liber de ludo aleae by J. Cardan published in 1663 but writen around 1564) studied dice games using ...
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2answers
120 views

Who introduced moments of a random variable first?

When, by whom and in which paper where moments of a random variable used first in probability theory?
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1answer
474 views

Poincaré and the baker: was the anecdote true?

There is a story featuring Henri Poincaré and an unscrupuolous baker. Every day Poincaré bought a piece of bread which should have weighted 1 kg. After an year, the mathematician brought the baker to ...
2
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1answer
412 views

Description of the Monte Carlo roulette wheel in 1913

It has been reported that on 18th August 1913, in a game of roulette at the Monte Carlo Casino, the ball fell on black 26 times in a row. This anecdote is often mentioned in the context of the gambler'...
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2answers
791 views

Did Karl Popper argue against Bayesian inference?

I am somewhat familiar with the works of Karl Popper and his opposition to using past data to induce prospects of future events, however disclaimed as uncertain, AKA historicism. He contributed to ...
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55 views

Carnap's last theory Of probability

According to Bar-Hillel, Carnap's coauthor in a 1952 report on probability, Carnap had, as of 1956 an unpublished but circulated theory distinguishing "random" refers to methods of production of ...
3
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1answer
206 views

First use of litte $o_p$ (little $o$ in probability) notation?

I have a follow up question from my previous question on math.SE, where I asked about the First use of little $o$ notation - for those who want to check - the answer goes back to Landau ($1909$), this ...
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1answer
78 views

Which version of the St Petersburg paradox is the original one?

There is are basically two versions of the St Petersburg paradox. They differ only on a minor point, namely in the amount that is paid. In one version, $n$ heads and then tails gives a payout of $2^{...
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1answer
469 views

Who developed Gaussian Mixture Model (GMM) and applied it to machine learning?

I searched about GMM (Gaussian mixture model), but only found that normal distribution was invented by Carl Friedrich Gauss. I'd like to know who contributed to the development of GMM itself, and to ...
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1answer
79 views

Name and history of probabilistic non-inevitability paradox?

A counterintuitive result in probability theory that may warrant the description of a veridical paradox is the fact that repeating an experiment with a nonzero chance of success infinitely often does ...
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3answers
1k views

Why wasn't probability developed in ancient Greece?

The modern axiomatic approach to probability was established by Kolmogorov nearly 70 years ago. According to Wikipedia, the first ideas connected to a mathematical theory of probability arose with ...
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2answers
323 views

What is the original source for Gelfand's problem on leading digits of the powers of 2?

The question of the distribution of the leading digits of the sequence $2^n$ is called Gelfand's problem or Gelfand's question. Is there any source that indicates Gelfand's own work on this, or the ...
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1answer
1k views

What is the history of moment generating functions, and the more general characteristic functions?

Moment generating functions provide an alternative specification for a probability distribution function (pdf), often making it very convenient to calculate expectations, variances, etc. of said pdf. ...
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59 views

Trying to learn some history of mathematics with parabolic Anderson model (PAM) as theme

I have been recently trying to find context and motivation for my Ph.D. Thesis in probability theory. I have not much background on the history of my theme. I just studied it aiming at solving a ...
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1answer
103 views

When was (and in what paper) Paley-Wiener integral invented?

When was (and in what paper) Paley-Wiener integral invented? Also, what was first? Paley-Wiener integral or Multiple Wiener Integral?
5
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1answer
287 views

Skorokhod's contribution to probability theory

I always thought of Skorokhod associated with the topology for convergence in the space of càdlàg (right continuous with left limits) functions in probability. But it seems that he made several other ...
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21 views

History of the delta potential barrier in Quantum Mechanics [closed]

I'm interested in finding something out about the history of the problem of the delta potential barrier in QM. Who was the first to propose this problem, and perhaps any particular motivation for it. ...
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2answers
142 views

History of delta barrier in quantum mechanics

I'm interested in finding something out about the history of the problem of the delta potential barrier in quantum mechanics. Which was the first study to propose this problem, and perhaps any ...
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1answer
1k views

First usage of binomial distribution

As stated in the article binomial distribution by britannica.com the binomial distribution was used by Jakob Bernoulli when he said that "the probability of $k$ ... outcomes in $n$ repetitions is ...
5
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1answer
1k views

Where does Markov operator come from?

I found this definition of "Markov operator" in the book Chaos, Fractals, and Noise by Lasota and Mackey. Denote by $L^1(\mu)$ the space of Lebesgue integrable functions according to the measure $\mu$...
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2k views

Who introduced random variables into probability?

I used to think that the answer is Kolmogorov. So the Shafer-Vovk's review of Kolmogorov's famous 1933 axiomatization of probability surprised me a bit:"Today, what Frechet and his contemporaries knew ...