xs bias when generating small number of events
When I generate 5000 events of a certain process 20 times with different random seeds I get these cross sections:
.15294E+00
.15200E+00
.15281E+00
.15235E+00
.15267E+00
.15244E+00
.15260E+00
.15171E+00
.15202E+00
.15180E+00
.15184E+00
.15042E+00
.15237E+00
.15250E+00
.15254E+00
.15306E+00
.15226E+00
.15146E+00
.15277E+00
.15179E+00
When I generate 1000 events of a certain process 20 times with different random seeds I get these cross sections:
.14930E+00
.14674E+00
.14699E+00
.14870E+00
.14798E+00
.14982E+00
.14802E+00
.14868E+00
.14823E+00
.14754E+00
.14894E+00
.14652E+00
.14767E+00
.14823E+00
.14852E+00
.14759E+00
.14916E+00
.14872E+00
.14927E+00
.14994E+00
Clearly, the average is not the same. Is this expected? I would expect that the cross sections I get when generating fewer events have the same average but a larger standard deviation.
The process I am generating is:
generate p p > w+ w+ p p QED=4 QCD=99, w+ > l+ vl
add process p p > w- w- p p QED=4 QCD=99, w- > l- vl~
Thanks.
Andrew
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