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Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant under certain transformation groups. This topic emphasises systematic development of formulas for calculating expected values associated with the geometric objects derived from random points, and can in part be viewed as a ...
The geometric distribution is the only memoryless discrete probability distribution. [4] It is the discrete version of the same property found in the exponential distribution . [ 1 ] : 228 The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success.
If X 1 and X 2 are independent geometric random variables with probability of success p 1 and p 2 respectively, then min(X 1, X 2) is a geometric random variable with probability of success p = p 1 + p 2 − p 1 p 2. The relationship is simpler if expressed in terms probability of failure: q = q 1 q 2.
In geometric probability theory, Wendel's theorem, named after James G. Wendel, gives the probability that N points distributed uniformly at random on an ()-dimensional hypersphere all lie on the same "half" of the hypersphere.
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.
A geometric stable distribution or geo-stable distribution is a type of leptokurtic probability distribution. Geometric stable distributions were introduced in Klebanov, L. B., Maniya, G. M., and Melamed, I. A. (1985).
One straightforward way to compute an ε-net with high probability is to take a sufficient number of random points, where the number of random points also depends only on ε. For example, in the diagram shown, any rectangle in the unit square containing at most three points in the 1/4-net has an area of at most 3/8 + 1/4 = 5/8.
Categorical probability; Category of Markov kernels; Category of measurable spaces; Central tendency; Chain rule (probability) Chvátal–Sankoff constants; Collectively exhaustive events; Complete filtration; Complex random variable; Complex random vector; Contiguity (probability theory) Continuum percolation theory; Convergence of Probability ...