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bio website physics.ox.ac.uk/qubit/…
location Oxford, United Kingdom
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visits member for 2 years
seen 21 hours ago

May
18
awarded  Supporter
May
18
comment Computing real integrals using the Residue Theorem where singularities are on the real line
You have $\int_0^\inf \frac{\sin(x)/x}{x^2+a^2}$. The function $\sin(x)/x$ does not have a pole at $x=0$ (strictly speaking it's undefined at $x=0$ but it has a holomorphic extension that includes the origin). So there are only two poles, $ia$ and $-ia$, both of which are not on the real line.
May
4
awarded  Student
Sep
11
revised Under what conditions is expectation value distributive?
added 282 characters in body
Sep
11
comment Under what conditions is expectation value distributive?
Thanks to everyone who tried to answer my question. I have now found a partial answer to my question. Unfortunately there is no guarantee that given marginal or conditional distributions for $X,Y$ and $X,Z$, there exists a joint distribution for $X,Y,Z$. This is why the distributive law does not always hold. The paper dealing with conditional distributions can be seen here. However, if anyone can lucidate the matter with a simple condition, the question is still open. I have also editted the question to make it clearer what I want.
Sep
10
comment Under what conditions is expectation value distributive?
Thanks for your answer Michael. Here is what I don't understand. Suppose $X,Y$ follow some measure $dp(x,y)$ (where $x,y$ are particular values of $X,Y$) and $X,Z$ follow $dq(x,y)$, where you can assume that $p$ and $q$ are densities. Now of course $\int dy p(x,y) = \int dz q(x,z)$. It is not obvious to me that $E(XY) + E(XZ) = int dx dy p(x,y) x y + \int dx dz q(x,z) x z = \int dx dy dz x(y+z) r(x,y,z) = E\bigl(X(Y+Z)\bigr)$. Does such extension of $p$ and $q$ always exist?
Sep
10
awarded  Editor
Sep
10
comment Under what conditions is expectation value distributive?
Thanks mjqxxxx, editted. I think it can't always be true because the violation of this property is needed to arrive at the violation of Bell inequalities in quantum mechanics.
Sep
10
revised Under what conditions is expectation value distributive?
edited title
Sep
10
asked Under what conditions is expectation value distributive?