This is the story of the averages, variances
of the random variable, x[1]
under the constraint Ax=b
for the matrix
[1 0 0 0 1 1 0 0]
[ ]
[0 1 0 0 1 0 0 1]
[ ]
[0 0 1 0 0 1 1 0]
[ ]
[0 0 0 1 0 0 1 1]
with the Poisson parameters given by, [1, 1, 1, 1, 1, 1, 1, 1]
for b from , [1, 1, 1, 1], to , [10, 10, 10, 10]
The sequence of averages is
[0.4285714286, 0.6985645933, 0.9119081564, 1.094111307, 1.255870848,
1.402863763, 1.538535373, 1.665165322, 1.784355840, 1.897284477]
This seems to be asymptotically
b 0.5740842188
0.4894036170 1.003316850 b
The sequence of standard deviations is
[0.7421624793, 0.8206751968, 0.8857493108, 0.9416894712, 0.9909727605,
1.035166075, 1.075328071, 1.112209871]
This seems to be asymptotically
b 0.3228996414
0.5631244813 1.001144724 b
This took, 16.645, seconds of CPU time