'''Jensen’s inequality, 젠센 부등식''' (kms) '''옌센 부등식''' (wpko)

오목볼록과 연관. - curr goto [[미적분,calculus#s-9]] <- 저기에도 설명 있음.
오목볼록과 매우 밀접. see https://suhak.tistory.com/221 (볼록 함수와 젠센 부등식)
[[볼록함수,convex_function]]

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''/*from [[https://www.di.univr.it/documenti/OccorrenzaIns/matdid/matdid648405.pdf this slide]] p2*/''

If $f$ is a [[볼록함수,convex_function]] and $X$ is a [[확률변수,random_variable]], then
 $Ef(X)\ge f(EX)$
Moreover(게다가/더욱이), if $f$ is strictly convex(순볼록), then equality implies that $X=EX$ with probability 1, i.e. $X$ is a constant.
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Twins:
[[https://terms.naver.com/entry.naver?docId=3405232&cid=47324&categoryId=47324 수학백과: 옌센 부등식]]
[[WpKo:옌센_부등식]]
{
기대값의 볼록함수와 볼록함수의 기대값 사이의 부등식 관계.
(see [[기대값,expected_value]], [[볼록함수,convex_function]])
}
[[WpEn:Jensen%27s_inequality]]
[[https://www.probabilitycourse.com/chapter6/6_2_5_jensen's_inequality.php]]
https://mathworld.wolfram.com/JensensInequality.html
https://encyclopediaofmath.org/wiki/Jensen_inequality

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Up: [[부등식,inequality]]