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Then the product process ,, … with = is a test supermartingale, and hence also an e-process (note that we already used this construction in the example described under "e-values as bets" above: for fixed , the e-values , were not dependent on past-data, but by using = ˘ | depending on the past, they became dependent on past data).
Since the probabilities must satisfy p 1 + ⋅⋅⋅ + p k = 1, it is natural to interpret E[X] as a weighted average of the x i values, with weights given by their probabilities p i. In the special case that all possible outcomes are equiprobable (that is, p 1 = ⋅⋅⋅ = p k), the weighted average is given by the standard average. In the ...
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The above image shows a table with some of the most common test statistics and their corresponding tests or models. A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic.
A test statistic shares some of the same qualities of a descriptive statistic, and many statistics can be used as both test statistics and descriptive statistics. However, a test statistic is specifically intended for use in statistical testing, whereas the main quality of a descriptive statistic is that it is easily interpretable. Some ...
The probability generating function of an almost surely constant random variable, i.e. one with (=) = and () = is G ( z ) = z c . {\displaystyle G(z)=z^{c}.} The probability generating function of a binomial random variable , the number of successes in n {\displaystyle n} trials, with probability p {\displaystyle p} of success in each trial, is
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A cheat sheet (also cheatsheet) or crib sheet is a concise set of notes used for quick reference. Cheat sheets were historically used by students without an instructor or teacher's knowledge to cheat on a test or exam. [1] In the context of higher education or vocational training, where rote memorization is not as important, students may be ...