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In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function.The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian).
Chernoff faces, invented by applied mathematician, statistician, and physicist Herman Chernoff in 1973, display multivariate data in the shape of a human face. The individual parts, such as eyes, ears, mouth, and nose represent values of the variables by their shape, size, placement, and orientation.
2 Set theory. 3 Descriptive geometry. ... Graph of a function. Logarithmic graph paper; ... Bullet graph; Chernoff faces; Control chart; Fan chart;
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Such inequalities are of importance in several fields, including communication complexity (e.g., in proofs of the gap Hamming problem [13]) and graph theory. [14] An interesting anti-concentration inequality for weighted sums of independent Rademacher random variables can be obtained using the Paley–Zygmund and the Khintchine inequalities. [15]
In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable = (()), where W is a "two-sided" Wiener process (or two-sided "Brownian motion") satisfying W(0) = 0.
Andrew Mattei Gleason (1921–2008) was an American mathematician who made fundamental contributions to widely varied areas of mathematics, including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in mathematics teaching at all levels.
It can be shown that such a graph exists for any g and k, and the proof is reasonably simple. Let n be very large and consider a random graph G on n vertices, where every edge in G exists with probability p = n 1/g −1. We show that with positive probability, G satisfies the following two properties: Property 1.