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P(A|B) may or may not be equal to P(A), i.e., the unconditional probability or absolute probability of A. If P(A|B) = P(A), then events A and B are said to be independent: in such a case, knowledge about either event does not alter the likelihood of each other. P(A|B) (the conditional probability of A given B) typically differs from P(B|A).
P(at least one estimation is bad) = 0.05 ≤ P(A 1 is bad) + P(A 2 is bad) + P(A 3 is bad) + P(A 4 is bad) + P(A 5 is bad) One way is to make each of them equal to 0.05/5 = 0.01, that is 1%. In other words, you have to guarantee each estimate good to 99%( for example, by constructing a 99% confidence interval) to make sure the total estimation ...
Assume that there is a counterexample: an integer n ≥ 2 such that there is no prime p with n < p < 2n. If 2 ≤ n < 427, then p can be chosen from among the prime numbers 3, 5, 7, 13, 23, 43, 83, 163, 317, 631 (each being the largest prime less than twice its predecessor) such that n < p < 2n. Therefore, n ≥ 427.
f(k, n, p) is monotone increasing for k < M and monotone decreasing for k > M, with the exception of the case where (n + 1)p is an integer. In this case, there are two values for which f is maximal: (n + 1) p and (n + 1) p − 1.
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In these bounds, K 1 and K 3 are constants that do not depend on a, b, or c, and K 2 is a constant that depends on ε (in an effectively computable way) but not on a, b, or c. The bounds apply to any triple for which c > 2. There are also theoretical results that provide a lower bound on the best possible form of the abc conjecture.
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Given a set , let denote the collection of all subsets of , including the empty set. An outer measure on is a set function: [,] such that . null empty set ...