The famous arithmetic mean-geometric mean inequality says that for any positive numbers a 1 , a 2 ,...,a n , Show that this inequality follows from Jensen’s inequality, by considering E log(X) for an...

Jensen´s inequality is a generalization of the fact that the graph of a one-variable real
convex function is always below the secant straight line that joins the extremes of the graph
over the corresponding interval. In equations, it can be written as:
ab
afxbbfax
xfbxa



)()()()(
)(
The above inequality is strict because we set bxa  . It might as well have been
stated:...