Jensen's Inequality: Mathematics, Convex function, Integral, Secant line, Probability theory, Random variable - Couverture souple

 
9786133760059: Jensen's Inequality: Mathematics, Convex function, Integral, Secant line, Probability theory, Random variable

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Jensen''s inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906. Given its generality, the inequality appears in many forms depending on the context, some of which are presented below. In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean after convex transformation; it is a simple corollary that the opposite is true of concave transformations.

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