Talk:Probability theory

sequences?

in the explanation of sample space, shouldn't the word "sequence" be "combination" as the order of the Californian voters does not matter?

Don't use F to mean two completely different things

I'm going to remove all references in this page to F as an event. It will only confuse people later when they see that F is a sigma-algebra. E=>A and F=>B is my suggested universal fix.

—

I concur. Additionally, it would be nice for Wikipedia articles to have consistency. Hence, I would also make the suggestion to use the script F that Probability space uses: "A probability space is a mathematical triplet $(\Omega ,{\mathcal {F}},P)$ or to use standard sigma algebra notation $(\Omega ,\Sigma ,P)$. Kdmckale (talk) 00:00, 29 September 2015 (UTC)

Probability is related to life

The article on probability theory is superficial. It uses jargon, while being disconnected from real life. I believe that the best foundation to theory of probability is laid out here:

[1]

The article is accompanied by free software pertinent to probability (combinatorics and statistics as well).

Ion Saliu, Probably At-Large

Now almost totally redundant, unless someone wants to merge something back in

To give a mathematical meaning to probability, consider flipping a "fair" coin. Intuitively, the probability that heads will come up on any given coin toss is "obviously" 50%; but this statement alone lacks mathematical rigor. Certainly, while we might expect that flipping such a coin 10 times will yield 5 heads and 5 tails, there is no guarantee that this will occur; it is possible, for example, to flip 10 heads in a row. What then does the number "50%" mean in this context?

One approach is to use the law of large numbers. In this case, we assume that we can perform any number of coin flips, with each coin flip being independent—that is to say, the outcome of each coin flip is unaffected by previous coin flips. If we perform N trials (coin flips), and let N_H be the number of times the coin lands heads, then we can, for any N, consider the ratio $N_{H} \over N$.

As N gets larger and larger, we expect that in our example the ratio $N_{H} \over N$ will get closer and closer to 1/2. This allows us to "define" the probability $\Pr(H)$ of flipping heads as the limit, as N approaches infinity, of this sequence of ratios:

$\Pr(H)=\lim _{N\to \infty }{N_{H} \over N}$

In actual practice, of course, we cannot flip a coin an infinite number of times; so in general, this formula most accurately applies to situations in which we have already assigned an a priori probability to a particular outcome (in this case, our assumption that the coin was a "fair" coin). The law of large numbers then says that, given Pr(H), and any arbitrarily small number ε, there exists some number n such that for all N > n,

$\left|\Pr(H)-{N_{H} \over N}\right|<\epsilon$

In other words, by saying that "the probability of heads is 1/2", we mean that if we flip our coin often enough, eventually the number of heads over the number of total flips will become arbitrarily close to 1/2; and will then stay at least as close to 1/2 for as long as we keep performing additional coin flips.

Note that a proper definition requires measure theory, which provides means to cancel out those cases where the above limit does not provide the "right" result (or is even undefined) by showing that those cases have a measure of zero.

The a priori aspect of this approach to probability is sometimes troubling when applied to real world situations. For example, in the play Rosencrantz & Guildenstern Are Dead by Tom Stoppard, a character flips a coin which keeps coming up heads over and over again, a hundred times. He can't decide whether this is just a random event—after all, it is possible (although unlikely) that a fair coin would give this result—or whether his assumption that the coin is fair is at fault.

Statistics or Mathamtics

The article claims that Probability Theory is a branch of mathematics. However, probability is fundamental to understanding data (statistics), just as arithmetic is fundamental to understanding mathematics, so it should be more appropriate to say that probability is a branch of statistics. Moreover, several US colleges consider Probability to be a subject within statistics, and are taught through the statistics department.--104.38.180.88 (talk) 18:28, 29 March 2018 (UTC)

history section

hello,

i dispute the first paragraph of the history section. the entire basis of the alleged philosophers being the creators of probability theory rests on a single article by an individual who is not a historian.

it is a wonder as to how this article was published and i believe the lack of citations nearly ten years later reflects the lack of agreement with the article.

further, five of the ten citations of the article that holds up an extraordinary claim (that flew in the face of all evidence until 2011, when this article was published) are from two authors.

indeed, a response to this article was made that shot down the entire claim. and i quote:

"The apparent independent references in Broemeling (2011) to al-Kadi (1992), Simon Singh (1999), and Mrayati, Alam, and al-Tayyan (2003) all trace back to a single reference, Mrayati, Alam, and al-Tayyan (1987). The 1987 date is taken from the Princeton University library catalog: no date appears on the item itself. An inspection of the references of the 1987 volume suggests the depth of scholarship. Page 381 of Mrayati, Alam, and al-Tayyan (1987) lists the five references presented in Roman characters rather than Arabic. Two are "Histoire de la Philosophe, volume 1" and "The New Encyclopedias Britannica, volume 6, USA" dates, publishers, and authors omitted in the original.

"A book review of the 1987 work appearing in Cryptologia, Krush (1993), is credulous as al-Kadi (1992) and Singh (1999). This is noteworthy because the basic English language reference that introduces the 1987 work, al-Kadi (1992) appears in Cryptologia, a journal edited by Kruh. Kruh (1997) reviews the successor volume to Mrayati, Alam, and al-Tayyan (1987). THe review is "based on a seven-page English abstract in the book" implying that Kruh does not read Arabic. One supposes that Kruh (1993) is based on the brief English abstract in Mrayati, Alam, and al-Tayyan (1987) and Kruh would only have that abstract and the five references to asses the work. Kruh rates both volumes as important for one's personal library."

"Perhaps al-Kind's work on secret writing and the development of statistics is not sufficiently recognized. Dramatic claims should at least search the modern record."

i will be removing this source from any history section mentioning it, and until a thorough and robust citation record is provided for its support, there is no justification for its retention or reintroduction.

outrageous no one looked at this until now. 198.53.108.48 (talk) 19:38, 4 August 2021 (UTC)

edit: further, for anyone who cares about this issue. i urge them to consult this diff to understand what is going on. the kahn citation was perverted to support the inadequately-sourced claims in the broemeling citation. this text was then recycled through multiple pages on wikipedia. i urge editors to take action.

• i have only edited pages that are typically read by the public.

i do not want to edit the corresponding history pages pertaining to specific cultures as they may hurl a term that was contrived in the past five or six years to support their position, instead of evidence.