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  2. St. Petersburg paradox - Wikipedia

    en.wikipedia.org/wiki/St._Petersburg_paradox

    Before Daniel Bernoulli's 1738 publication, mathematician Gabriel Cramer from Geneva had already in 1728 found parts of this idea (also motivated by the St. Petersburg paradox), stating that the mathematicians estimate money in proportion to its quantity, and men of good sense in proportion to the usage that they may make of it.

  3. Bernoulli distribution - Wikipedia

    en.wikipedia.org/wiki/Bernoulli_distribution

    The Bernoulli distribution is a special case of the binomial distribution with = [4] The kurtosis goes to infinity for high and low values of p , {\displaystyle p,} but for p = 1 / 2 {\displaystyle p=1/2} the two-point distributions including the Bernoulli distribution have a lower excess kurtosis , namely −2, than any other probability ...

  4. Exchangeable random variables - Wikipedia

    en.wikipedia.org/wiki/Exchangeable_random_variables

    The von Neumann extractor is a randomness extractor that depends on exchangeability: it gives a method to take an exchangeable sequence of 0s and 1s (Bernoulli trials), with some probability p of 0 and = of 1, and produce a (shorter) exchangeable sequence of 0s and 1s with probability 1/2.

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  6. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    The expectation of conditioned on the event that lies in an interval [,] is given by ⁡ [< <] = () (), where and respectively are the density and the cumulative distribution function of . For b = ∞ {\textstyle b=\infty } this is known as the inverse Mills ratio .

  7. Bernoulli process - Wikipedia

    en.wikipedia.org/wiki/Bernoulli_process

    A Bernoulli process is a finite or infinite sequence of independent random variables X 1, X 2, X 3, ..., such that for each i, the value of X i is either 0 or 1; for all values of , the probability p that X i = 1 is the same. In other words, a Bernoulli process is a sequence of independent identically distributed Bernoulli trials.

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  9. 3 Stock Market Mistakes Investors Should Avoid in 2025 - AOL

    www.aol.com/3-stock-market-mistakes-investors...

    AAPL Market Cap data by YCharts. Other noteworthy examples include selling out of oil and gas stocks during the downturn of 2020. In the last four years, the energy sector is up 129%.

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