Intuitive interpretation of negative probabilities I have heard that in quantum physics negative probabilities show up in certain distributions. 
Could you give an example that aids int he intuitional interpretation of a negative probability? 
For example, what does $X \sim N(0,1) -\delta$ mean, and how does it relate to $Y \sim N(0,1)$. Can we say anything about the relationship between $Y$ and $X$?
 A: I don't think anyone has a clear understanding of negative probabilities. 
There seems to be a rather good axionmatic background (http://physics.bu.edu/~youssef/quantum/Burgin-1.pdf) and the definition of an extended probability space ("extended" means either positive or negative) is rather well defined mathematically. There are events and anti-events that cancel eachother when elements of a set : $\{w,-w\}\approx\emptyset$. 
Honestly I can't validate the content of the acticle personnaly since I read superficially and find it hard to read.
But what does it mean intuitively ?
Assume you have two cases $A$ and $\overline{A}$ (not $A$) each with probability 0.5 to make it simple. If an event $X$ has probabiliy 0.3 when $A$ is true ($P(X|A)=0.3$), and has probability -0.3 when $A$ is false ($P(X|\overline{A})=-0.3$), or equivalently the antievent $-X$ has probability 0.3 when not $A$, then  as a whole, X has probability $0$. Thus X never happens.
I don't think anyone on earth understands it further than this.
You can find it explained here by Feynman : https://johncarlosbaez.wordpress.com/2013/07/19/negative-probabilities/  . Maybe the most important motivation for negative probabilities is Quantum Mechanics and most significantly the Wiegner quasi-distribution.
It's like a cancelation happens : $-X$ cancels $X$. This is rather intuitive. But this happens between two cases ($A$ and $\overline{A}$) that cannot happen together. I've never read a text giving an intuivie catch of this. It is directly related to some of the greatest mystery of Quantum Mechanics. 
