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  2. Variance - Wikipedia

    en.wikipedia.org/wiki/Variance

    Download as PDF; Printable version ... variance is the expected value of the squared deviation from the mean of ... as the expectation value of ~ is smaller than the ...

  3. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    Expected values can also be used to compute the variance, by means of the computational formula for the variance ⁡ = ⁡ [] (⁡ []). A very important application of the expectation value is in the field of quantum mechanics.

  4. Conditional variance - Wikipedia

    en.wikipedia.org/wiki/Conditional_variance

    In words: the variance of Y is the sum of the expected conditional variance of Y given X and the variance of the conditional expectation of Y given X. The first term captures the variation left after "using X to predict Y", while the second term captures the variation due to the mean of the prediction of Y due to the randomness of X.

  5. Gamma distribution - Wikipedia

    en.wikipedia.org/wiki/Gamma_distribution

    It is the conjugate prior for the precision (i.e. inverse of the variance) of a normal distribution. It is also the conjugate prior for the exponential distribution . In phylogenetics , the gamma distribution is the most commonly used approach to model among-sites rate variation [ 43 ] when maximum likelihood , Bayesian , or distance matrix ...

  6. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    [18] [19] Geary has shown, assuming that the mean and variance are finite, that the normal distribution is the only distribution where the mean and variance calculated from a set of independent draws are independent of each other. [20] [21] The normal distribution is a subclass of the elliptical distributions.

  7. Law of total variance - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_variance

    In probability theory, the law of total variance [1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law, [2] states that if and are random variables on the same probability space, and the variance of is finite, then

  8. Log-normal distribution - Wikipedia

    en.wikipedia.org/wiki/Log-normal_distribution

    The pdf and cdf of the function ... The partial expectation formula has applications in insurance and ... Since the sample mean and variance are independent, ...

  9. Law of total expectation - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_expectation

    The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value ⁡ is defined, and is any random variable on the same probability space, then