Questions tagged [probability]
55 questions
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Is there any evidence De Morgan abandoned probability theory due to it being "too tricky/non-intuitive/difficult"?
During a brief conversation in Ten Fold, whuber pointed out:
I recall reading long ago that Augustus DeMorgan abandoned probability theory after much study, finding it too tricky/non-intuitive/difficult; but I have been unable to find an…
User1865345
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Was Poisson and other distributions found by solving applied problems or by playing around theoretically?
I'm trying to get a sense of how statistical distributions arose and I'm using Poisson as an example. The folklore I grew up with says that Gauss arrived at the normal distribution while trying to account for errors in astronomical measurements. And…
TonyK
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2
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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's fallacy (see the wiki).
I am looking for…
PatrickT
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What advances in statistics did measure-theoretic probability theory allow?
I've Googled this question in several different ways and I get a lot of hits, but nothing answering the question.
To flesh out the subject line a little, I'm interested in understanding where, in the big scheme of things, Kolmogorov's 1933 work…
TonyK
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History of cdf as to how it was defined prior Kolmogorov and how the paradigm shifted from $<$ case to $\leq $ case
Cumulative distribution function is pretty much known and well covered from undergrad to grad probability texts. Specifically if $\mathbf P$ is a probability measure on $(\mathbb R, \mathfrak B_\mathbb R),$ then cdf is defined as
$$\mathsf F(x):=…
User1865345
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2
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Origin of a problem with three dice
I am working on a set of problems with historic context, and I do not seem to be able to retrack, why I consider this problem historic:
Three dice are thrown each round. The question is, how often does one have to throw the three dice until each of…
Peter Strouvelle
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Is the number of PhDs who berated Marilyn von Savant's answer to the Monty Hall problem exaggerated?
Yet the naive definition,
even when inappropriate, has a powerful hold on people's intuitions. When Marilyn
vos Savant presented a correct solution to the Monty Hall problem in her column for Parade magazine in 1990, she received thousands upon…
user3478
2
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Why's the true positive rate termed Sensitivity and true negative rate Specificity, not vice versa?
To wit, what's "Sensitive" about True Positive Rates, and "Specific" about True Negative Rates?
Why weren't these Metaphors or Imports reversed? Why wasn't "Sensitive" termed to signify True Negative Rates, and "Specific" True Positive Rates…
user3478
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Probability in Ancient Greece and Rome -- Dice vs Divination?
My understanding is that probability theory is 16th or 17th century but games of chance existed 2000 years ago -- even if more complex probabilities were not understood by ancients, surely they understood that some numbers were more likely?
And…
releseabe
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Where is conditional probability in Bayes' paper
The modern way to get to Bayes' theorem is through conditional probability. How did Bayes get to it? I've read, with crossed eyes, his 1763 paper and I cannot see conditional probability or his theorem in any recognizable form. Price's appendix…
TonyK
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If Math is Based on Unprovable Axioms and these Axioms can't be Proven - Why Does Math "Work" so Well?
If Math is Based on Unprovable Axioms and can't be Proven - Why Does Math "Work" so Well?
I have heard that both Mathematics and Religions are based on "axioms" that are by definition unprovable. I have also heard some people argue that Mathematics,…
stats_noob
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Who was the first English author that incorporated Markov's Law of Large Numbers and its derivation?
There is a theorem due to Markov, called Markov's Law of Large Numbers which goes by:
The weak law of large numbers holds if for some $\delta > 0,$ all the mathematical expectations $\mathbb E\left(|X_i|^{1+\delta}\right);~ i = 1,2,\ldots$ exist…
User1865345
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