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  2. Law of truly large numbers - Wikipedia

    en.wikipedia.org/wiki/Law_of_truly_large_numbers

    The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e. unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. [1]

  3. Law of the unconscious statistician - Wikipedia

    en.wikipedia.org/wiki/Law_of_the_unconscious...

    In probability theory and statistics, the law of the unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability distribution of X. The form of the law depends on the type of random variable X in question.

  4. Free probability - Wikipedia

    en.wikipedia.org/wiki/Free_probability

    Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence property is the analogue of the classical notion of independence , and it is connected with free products .

  5. Probability - Wikipedia

    en.wikipedia.org/wiki/Probability

    Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...

  6. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would "expect" to get in reality.

  7. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    A discrete probability distribution is the probability distribution of a random variable that can take on only a countable number of values [15] (almost surely) [16] which means that the probability of any event can be expressed as a (finite or countably infinite) sum: = (=), where is a countable set with () =.

  8. Likelihood function - Wikipedia

    en.wikipedia.org/wiki/Likelihood_function

    The specific calculation of the likelihood is the probability that the observed sample would be assigned, assuming that the model chosen and the values of the several parameters θ give an accurate approximation of the frequency distribution of the population that the observed sample was drawn

  9. Uncorrelatedness (probability theory) - Wikipedia

    en.wikipedia.org/wiki/Uncorrelatedness...

    In probability theory and statistics, two real-valued random variables, , , are said to be uncorrelated if their covariance, ⁡ [,] = ⁡ [] ⁡ [] ⁡ [], is zero. If two variables are uncorrelated, there is no linear relationship between them.