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Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. 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.
If X is a nonnegative random variable and a > 0, and U is a uniformly distributed random variable on [,] that is independent of X, then [4] (). Since U is almost surely smaller than one, this bound is strictly stronger than Markov's inequality.
PowerPoint version 14.0 (2010, 2011 for Mac) could read and write Transitional, and also read but not write Strict. PowerPoint version 15.0 and later (beginning 2013, 2016 for Mac) can read and write both Transitional and Strict formats. The reason for the two variants was explained by Microsoft: [278]