This is the story of the averages and variance of the random variable, x[1] under the constraint Ax=b for the matrix [1 0 0 1 1] [ ] [0 1 1 1 1] with the Poisson parameters given by, [1, 1, 1, 1, 1] for b from , [3, 3], to , [200, 200] The sequence of averages is [1.147058824, 1.397129187, 1.620310479, 1.823816313, 2.012121721, 2.188222613, 2.354240190, 2.511741696, 2.661924355, 2.805727525, 2.943904556, 3.077070746, 3.205736458, 3.330330645, 3.451217995, 3.568711681, 3.683083026, 3.794568953, 3.903377808, 4.009693970, 4.113681550, 4.215487382, 4.315243467, 4.413068999, 4.509072035, 4.603350902, 4.695995385, 4.787087731, 4.876703505, 4.964912327, 5.051778512, 5.137361611, 5.221716901, 5.304895795, 5.386946213, 5.467912907, 5.547837744, 5.626759963, 5.704716396, 5.781741677, 5.857868413, 5.933127352, 6.007547528, 6.081156389, 6.153979916, 6.226042735, 6.297368209, 6.367978528, 6.437894791, 6.507137079, 6.575724525, 6.643675369, 6.711007022, 6.777736115, 6.843878548, 6.909449531, 6.974463631, 7.038934805, 7.102876434, 7.166301363, 7.229221921, 7.291649958, 7.353596863, 7.415073598, 7.476090709, 7.536658358, 7.596786335, 7.656484082, 7.715760705, 7.774624996, 7.833085444, 7.891150249, 7.948827340, 8.006124383, 8.063048794, 8.119607752, 8.175808209, 8.231656897, 8.287160343, 8.342324871, 8.397156616, 8.451661532, 8.505845394, 8.559713812, 8.613272231, 8.666525945, 8.719480096, 8.772139684, 8.824509572, 8.876594490, 8.928399041, 8.979927705, 9.031184843, 9.082174705, 9.132901429, 9.183369048, 9.233581493, 9.283542596, 9.333256095, 9.382725635, 9.431954775, 9.480946985, 9.529705654, 9.578234091, 9.626535528, 9.674613120, 9.722469952, 9.770109038, 9.817533323, 9.864745687, 9.911748947, 9.958545857, 10.00513911, 10.05153135, 10.09772514, 10.14372302, 10.18952746, 10.23514088, 10.28056564, 10.32580408, 10.37085846, 10.41573102, 10.46042393, 10.50493934, 10.54927935, 10.59344601, 10.63744134, 10.68126733, 10.72492590, 10.76841898, 10.81174841, 10.85491604, 10.89792367, 10.94077306, 10.98346595, 11.02600404, 11.06838900, 11.11062247, 11.15270607, 11.19464138, 11.23642995, 11.27807332, 11.31957300, 11.36093045, 11.40214713, 11.44322447, 11.48416388, 11.52496672, 11.56563437, 11.60616815, 11.64656938, 11.68683935, 11.72697933, 11.76699057, 11.80687431, 11.84663176, 11.88626410, 11.92577251, 11.96515815, 12.00442215, 12.04356564, 12.08258971, 12.12149546, 12.16028395, 12.19895624, 12.23751336, 12.27595634, 12.31428619, 12.35250390, 12.39061044, 12.42860679, 12.46649389, 12.50427268, 12.54194408, 12.57950901, 12.61696836, 12.65432302, 12.69157386, 12.72872174, 12.76576751, 12.80271201, 12.83955606, 12.87630048, 12.91294607, 12.94949363, 12.98594394, 13.02229776, 13.05855588, 13.09471902, 13.13078795, 13.16676338, 13.20264605, 13.23843666, 13.27413593, 13.30974454, 13.34526319, 13.38069256, 13.41603331] This seems to be asymptotically b 0.5222075924 0.8503390955 0.9999848354 b 1/2 If we assume that this grows like a constant times, b then it is reasobale that the asymptotics of the averages is 1/2 0.9486568128 b The sequence of standard deviations is [0.7329373997, 0.8067842645, 0.8684949476, 0.9218881411, 0.9691462517, 1.011661594, 1.050387042, 1.086007348, 1.119032785, 1.149854569, 1.178779627, 1.206053430, 1.231875524, 1.256410424, 1.279795435, 1.302146404, 1.323562011, 1.344127042, 1.363914909, 1.382989622, 1.401407347, 1.419217655, 1.436464531, 1.453187190, 1.469420754, 1.485196812, 1.500543887, 1.515487816, 1.530052097, 1.544258157, 1.558125590, 1.571672378, 1.584915046, 1.597868834, 1.610547821, 1.622965044, 1.635132601, 1.647061736, 1.658762925, 1.670245942, 1.681519921, 1.692593414, 1.703474440, 1.714170525, 1.724688747, 1.735035770, 1.745217875, 1.755240994, 1.765110725, 1.774832372, 1.784410953, 1.793851227, 1.803157711, 1.812334693, 1.821386250, 1.830316269, 1.839128442, 1.847826294, 1.856413188, 1.864892333, 1.873266797, 1.881539513, 1.889713287, 1.897790806, 1.905774647, 1.913667275, 1.921471062, 1.929188281, 1.936821114, 1.944371665, 1.951841946, 1.959233905, 1.966549408, 1.973790259, 1.980958192, 1.988054877, 1.995081934, 2.002040915, 2.008933328, 2.015760621, 2.022524201, 2.029225423, 2.035865599, 2.042445998, 2.048967848, 2.055432340, 2.061840626, 2.068193821, 2.074493009, 2.080739236, 2.086933522, 2.093076854, 2.099170189, 2.105214459, 2.111210566, 2.117159389, 2.123061780, 2.128918569, 2.134730563, 2.140498544, 2.146223276, 2.151905502, 2.157545943, 2.163145304, 2.168704270, 2.174223508, 2.179703668, 2.185145386, 2.190549277, 2.195915947, 2.201245981, 2.206539952, 2.211798421, 2.217021933, 2.222211021, 2.227366205, 2.232487994, 2.237576884, 2.242633358, 2.247657892, 2.252650947, 2.257612978, 2.262544426, 2.267445721, 2.272317290, 2.277159546, 2.281972894, 2.286757729, 2.291514438, 2.296243405, 2.300944999, 2.305619582, 2.310267514, 2.314889141, 2.319484806, 2.324054845, 2.328599586, 2.333119350, 2.337614454, 2.342085205, 2.346531908, 2.350954859, 2.355354354, 2.359730672, 2.364084099, 2.368414908, 2.372723370, 2.377009751, 2.381274308, 2.385517300, 2.389738977, 2.393939584, 2.398119364, 2.402278556, 2.406417391, 2.410536099, 2.414634905, 2.418714030, 2.422773694, 2.426814108, 2.430835482, 2.434838025, 2.438821938, 2.442787420, 2.446734669, 2.450663877, 2.454575235, 2.458468929, 2.462345142, 2.466204055, 2.470045848, 2.473870692, 2.477678764, 2.481470228, 2.485245255, 2.489004007, 2.492746648, 2.496473334, 2.500184223, 2.503879471, 2.507559228, 2.511223643, 2.514872865, 2.518507040, 2.522126309, 2.525730812, 2.529320692, 2.532896081, 2.536457117, 2.540003930, 2.543536655, 2.547055418, 2.550560347, 2.554051568, 2.557529203, 2.560993375, 2.564444205, 2.567881809] This seems to be asymptotically b 0.2622690252 0.6421229868 0.9999954957 b (1/4) If we assume that this grows like a constant times, b then it is reasobale that the asymptotics of the averages is (1/4) 0.6828377642 b This took, 2.217, seconds of CPU time