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Download as PDF; Printable version; In other projects ... Probability measure; Random variable. ... Template documentation
In case (1) above, the conditional probability that the longitude λ lies in a set E given that φ = 0 can be written P(λ ∈ E | φ = 0). Elementary probability theory suggests this can be computed as P(λ ∈ E and φ = 0)/P(φ = 0), but that expression is not well-defined since P(φ = 0) = 0.
In fact, the discrete case (although without the restriction to probability measures) is the first step in proving the general measure-theoretic formulation, as the general version follows therefrom by an application of the monotone convergence theorem. [7] Without any major changes, the result can also be formulated in the setting of outer ...
In probability theory, Markov's inequality gives an upper bound on the probability that a non-negative random variable is greater than or equal to some positive constant. Markov's inequality is tight in the sense that for each chosen positive constant, there exists a random variable such that the inequality is in fact an equality.
The term measure here refers to the measure-theoretic approach to probability. Violations of unit measure have been reported in arguments about the outcomes of events [2] [3] under which events acquire "probabilities" that are not the probabilities of probability theory. In situations such as these the term "probability" serves as a false ...
When the underlying measure on (, ()) is finite, the distribution function in Definition 3 differs slightly from the standard definition of the distribution function (in the sense of probability theory) as given by Definition 2 in that for the former, = while for the latter, () = = ().
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