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In mathematics, concentration inequalities provide probability bounds on how a random variable deviates from some value (e.g., its expectation). The laws of large numbers of classical probability theory state that sums of independent random variables are, under very mild conditions, close to their expectation with a large probability. Such sums are the most basic examples of random variables concentrated around their mean. Recent results shows that such behavior is shared by other functions of independent random variables. ==Markov's inequality== If ''X'' is a nonnegative random variable and ''a'' > 0, then : Proof can be found here. We can extend Markov's inequality to a strictly increasing and non-negative function . We have : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「concentration inequality」の詳細全文を読む スポンサード リンク
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