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  2. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    When "E" is used to denote "expected value", authors use a variety of stylizations: the expectation operator can be stylized as E (upright), E (italic), or (in blackboard bold), while a variety of bracket notations (such as E(X), E[X], and EX) are all used. Another popular notation is μ X.

  3. Exponential distribution - Wikipedia

    en.wikipedia.org/wiki/Exponential_distribution

    In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...

  4. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    For instance, e x can be defined as (+). Or e x can be defined as f x (1), where f x : R → B is the solution to the differential equation ⁠ df x / dt ⁠ (t) = x f x (t), with initial condition f x (0) = 1; it follows that f x (t) = e tx for every t in R.

  5. Conditional expectation - Wikipedia

    en.wikipedia.org/wiki/Conditional_expectation

    The related concept of conditional probability dates back at least to Laplace, who calculated conditional distributions.It was Andrey Kolmogorov who, in 1933, formalized it using the Radon–Nikodym theorem. [1]

  6. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    n = 1 that yield a minimax approximation or bound for the closely related Q-function: Q(x) ≈ Q̃(x), Q(x) ≤ Q̃(x), or Q(x) ≥ Q̃(x) for x ≥ 0. The coefficients {(a n,b n)} N n = 1 for many variations of the exponential approximations and bounds up to N = 25 have been released to open access as a comprehensive dataset. [16]

  7. Variance - Wikipedia

    en.wikipedia.org/wiki/Variance

    This implies that in a weighted sum of variables, the variable with the largest weight will have a disproportionally large weight in the variance of the total. For example, if X and Y are uncorrelated and the weight of X is two times the weight of Y, then the weight of the variance of X will be four times the weight of the variance of Y.

  8. Hat notation - Wikipedia

    en.wikipedia.org/wiki/Hat_notation

    In statistics, a circumflex (ˆ), called a "hat", is used to denote an estimator or an estimated value. [1] For example, in the context of errors and residuals , the "hat" over the letter ε ^ {\displaystyle {\hat {\varepsilon }}} indicates an observable estimate (the residuals) of an unobservable quantity called ε {\displaystyle \varepsilon ...

  9. Likelihood function - Wikipedia

    en.wikipedia.org/wiki/Likelihood_function

    More generally, for each value of , we can calculate the corresponding likelihood. The result of such calculations is displayed in Figure 1. The result of such calculations is displayed in Figure 1. The integral of L {\textstyle {\mathcal {L}}} over [0, 1] is 1/3; likelihoods need not integrate or sum to one over the parameter space.