Timeline for Proving convexity of the expected logarithm of binomial distribution

9 events

when toggle format	what		by	license	comment
Mar 16 at 22:42	comment	added	RotemBZ		Thank you for the answer @IosifPinelis. Great solution!
Mar 16 at 22:39	vote	accept	RotemBZ
Mar 14 at 12:32	history	edited	YCor	CC BY-SA 4.0	formatting, added tag
S Mar 14 at 12:32	history	suggested	Laithy	CC BY-SA 4.0	changed "for some integer" to "for an arbitrary integer" to improve clarity.
Mar 14 at 12:09	answer	added	Iosif Pinelis		timeline score: 2
Mar 13 at 22:09	review	Suggested edits
S Mar 14 at 12:32
Mar 13 at 21:57	comment	added	Christian Remling		We can write $f(x)=x\log(n+1) + E\overline{X}\log \overline{X}$, with $\overline{X} =S/(n+1)$, $S\sim B(n+1,x)$. Of course, the linear term does not affect the convexity (or lack of it). This is circumstantial evidence that your conjecture is true since at least for large $n$, the CLT shows that the second term is $\simeq x\log x$, which is a convex function.
S Mar 13 at 18:22	review	First questions
Mar 13 at 22:10
S Mar 13 at 18:22	history	asked	RotemBZ	CC BY-SA 4.0