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 Apr 20 asked Distribution of sample minimum after bivariate selection (double truncation) Feb 29 accepted Derivative of joint probability wrt mean Feb 29 comment Derivative of joint probability wrt mean Fantastic. Thanks!! Feb 29 revised Derivative of joint probability wrt mean Typo Feb 29 comment Derivative of joint probability wrt mean thanks for this. It is a great answer to my question as it was originally posted. However, I made a very silly typo... $\mu$ was meant to be the mean, not variance of $Y$! Hence the title of the question... I've edited it to avoid confusion. Apologies for the awful oversight Feb 29 comment Derivative of joint probability wrt mean Oh, thanks!! That was a terrible typo! I've fixed the question now Feb 29 revised Derivative of joint probability wrt mean Huge Typo!; added 59 characters in body Feb 29 comment Derivative of joint probability wrt mean @ByronSchmuland: Not sure I follow you... just to restate, my conjecture is that $\Pr(Ya)$ is strictly decreasing in $\mu$ for all $b,a,\rho$. Your point is that this is not possible? Feb 29 revised Derivative of joint probability wrt mean added 48 characters in body Feb 29 awarded Custodian Feb 29 reviewed Approve Parameterizing conditional expectations in terms of regression coefficients (gaussian case) Feb 29 comment Derivative of joint probability wrt mean Yes. With correlation noted $\rho{xy}$. I edited the question so that this is clear. Feb 29 revised Derivative of joint probability wrt mean added 7 characters in body Feb 29 asked Derivative of joint probability wrt mean Feb 29 asked Parameterizing conditional expectations in terms of regression coefficients (gaussian case) May 21 revised Conditions for positive dependence added 68 characters in body May 20 awarded Teacher Jul 2 awarded Curious Jun 5 comment For which joint distributions is a conditional expectation an additive function? Thanks, yes. Hmâ€¦ Would you know of a characterisation for the (stronger) linear case? Jun 5 comment For which joint distributions is a conditional expectation an additive function? True. I only need that it is separable (additively decomposed)