Timeline for Derivatives of conditional expectations

6 events

when toggle format	what		by	license	comment
Mar 19, 2012 at 1:54	vote	accept	Tom LaGatta
Mar 18, 2012 at 8:35	answer	added	Yves		timeline score: 3
Dec 13, 2011 at 17:36	history	edited	Tom LaGatta	CC BY-SA 3.0	added 266 characters in body
Dec 13, 2011 at 17:35	comment	added	Tom LaGatta		Thanks, fedja. Bimodality seems like a reasonably robust way to construct counterexamples. Perhaps a natural assumption would be to assume that all the density functions are log-concave (i.e., $x \mapsto -\log f(x)$ is a convex function). This would include Gaussian density functions (though not power-law).
Dec 13, 2011 at 2:55	comment	added	fedja		Imagine $X$ that is bimodal: it is about $0$ or $1$ with probability $1/2$ each (you can smear that to get continuous density). Imagine $Y=\pm 0.1$ with probability $1/2$ for each sign (again, smear a bit) and $Z$ smeared over a huge interval uniformly. Then the condition $B=b$ tells next to nothing about $X$ but when $A=0.1$, you know that $Y$ is $0.1$ (otherwise there is no chance to get there) and when $A=0.9$, you are pretty certain that $Y=-0.1$. Bad, isn't it? As to simple conditions, what terms are allowed?
Dec 13, 2011 at 1:35	history	asked	Tom LaGatta	CC BY-SA 3.0