Implement detector response with conditional pdf

Roofit and RooStats
1

I am trying to implement this pdf

P [ reco ] = Int P[reco | true] * P [ true ] dtrue

for simplicity P [ true ] is a narrow guassian and P [ reco | true ] is a wide gaussian centered to true.

P [ true ] = Norm [ true | mu = 90E3, sigma = 1E3 ]
P [ reco | true ] = Norm [ reco | mu = true, sigma = 1E4 ]

here my code:

    RooRealVar mreco("mreco", "m_{reco} (GeV)", 30E3, 120E3);
    RooRealVar mtrue("mtrue", "m_{true} (GeV)", 30E3, 120E3);

    RooRealVar true_width("true_width", "true width", 1E3, 0.001, 50E3);
    RooGaussian true_dist("true_dist", "true", mtrue, RooConst(90E3), true_width);

    RooRealVar resolution("resolution", "resolution", 1E4, 0.001, 100E3);
    RooGaussian response("response", "response", mreco, mtrue, resolution);

    RooProdPdf result("result", "result", true_dist, Conditional(response, mreco));

    RooPlot* true_frame = mtrue.frame();
    true_dist.plotOn(true_frame);

    RooPlot* reco_frame = mreco.frame();
    result.plotOn(reco_frame);

    true_frame->Draw();

    c2 = new TCanvas();


    reco_frame->Draw();

I really don’t understand why the result is not centered at 90E3, but it is centered around 75E3