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At about the same time, Makarov, [6] and independently, Rüschendorf [7] solved the problem, originally posed by Kolmogorov, of how to find the upper and lower bounds for the probability distribution of a sum of random variables whose marginal distributions, but not their joint distribution, are known.
Chebyshev's inequality requires the following information on a random variable : . The expected value [] is finite.; The variance [] = [( [])] is finite.; Then, for every constant >,
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
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 ...
Decision boundaries can be approximations of optimal stopping boundaries. [ 2 ] The decision boundary is the set of points of that hyperplane that pass through zero. [ 3 ] For example, the angle between a vector and points in a set must be zero for points that are on or close to the decision boundary.