Integral w/ DiracDelta gives different results on different versions

Posted 5 months ago
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 I have access to Mathematica 9.0.0 and Mathematica 10.4.0. Recently I discovered that computing the same exact integral gives different answers in different versions of Mathematica. The integral involves the product of a DiracDelta function and a Gaussian density. I believe the result in 10.4 is incorrect and that there is a [B-word] in this version. I have emailed technical support about the issue. In the meanwhile, can someone with access to Mathematica 11 check whether this issue is still present?Code in question: Assuming[ Element[a, Reals] && Element[y, Reals] && Element[z, Reals], Integrate[ DiracDelta[y - (x + a)/z] PDF[NormalDistribution[0, s], x], {x, -Infinity, Infinity}]] Output in Mathematica 9.0.0: (E^(-((a - y z)^2/(2 s^2))) Abs[z])/(Sqrt[2 \[Pi]] s) Output in Mathematica 10.4.0: (1 + E^(-((a - y z)^2/(2 s^2))) + Abs[z])/(Sqrt[2 \[Pi]] s) Plotting the two functions will confirm that they are not mathematically equivalent (and that the result from 10.4 does not make any sense).Thanks for your input!
 Hi MMA says:  $Version (* "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)"*) Integrate[DiracDelta[y - (x + a)/z] PDF[NormalDistribution[0, s], x], {x, -Infinity, Infinity}, Assumptions -> {{a, y, z} \[Element] Reals, s > 0}] (* (E^(-((a - y z)^2/(2 s^2))) Abs[z])/(Sqrt[2 \[Pi]] s) *) If you don't have Mathematica 11.3,you can try for free,you must only sign-in.Regards,MI Answer Posted 5 months ago  Hi, thanks for checking! Looks like they got the bug sorted out. And I had no idea it's possible to play around with the latest version online, that's also great to know! Answer Posted 5 months ago  In[1]:=$Version Out[1]= "10.2.0 for Microsoft Windows (64-bit) (July 28, 2015)" In[2]:= Assuming[ Element[a, Reals] && Element[y, Reals] && Element[z, Reals], Integrate[ DiracDelta[y - (x + a)/z] PDF[NormalDistribution[0, s], x], {x, -Infinity, Infinity}]] Out[2]= (E^(-((a - y z)^2/(2 s^2))) Abs[z])/(Sqrt[2 \[Pi]] s) In[1]:= $Version Out[1]= "11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)" In[2]:= Assuming[ Element[a, Reals] && Element[y, Reals] && Element[z, Reals], Integrate[ DiracDelta[y - (x + a)/z] PDF[NormalDistribution[0, s], x], {x, -Infinity, Infinity}]] Out[2]= (E^(-((a - y z)^2/(2 s^2))) Abs[z])/(Sqrt[2 \[Pi]] s)$Version "8.0 for Microsoft Windows (64-bit) (October 7, 2011)" Assuming[Element[a, Reals] && Element[y, Reals] && Element[z, Reals], Integrate[ DiracDelta[y - (x + a)/z] PDF[NormalDistribution[0, s], x], {x, -Infinity, Infinity}]] (E^(-((a - y z)^2/(2 s^2))) Abs[z])/(Sqrt[2 \[Pi]] s)