Hi List, I'm new to Numpy and I'm a little confused about the behavior of numpy.random.multivariate_normal(). I'm not sure I'm passing the variances correctly. My goal is to sample from a bivariate normal, but the kooky behavior shows up when I sample from a univariate distribution. In short, the multivariate normal function doesn't seem to give me values in the appropriate ranges. Here's an example of what I mean. In[1]: from numpy.random import normal, multivariate_normal In [2]: normal(100, 100, 10) Out[2]: array([ 258.62344586, 70.16378815, 49.46826997, 49.58567724, 182.68652256, 226.67292034, 92.03801549, 18.2686146 , 94.09104313, 80.35697507]) The samples look about right to me. But then when I try to do the same using the multivariate_normal, the values it draws look too close to the mean. In [3]: multivariate_normal([100], [[100]], 10) Out[3]: array([[ 109.10083984], [ 97.43526716], [ 108.43923772], [ 97.87345947], [ 103.405562 ], [ 110.2963736 ], [ 103.96445585], [ 90.58168544], [ 91.20549222], [ 104.4051761 ]]) These values all fall within 10 units of the mean. In [4]: multivariate_normal([100], [[1000]], 10) Out[4]: array([[ 62.04304611], [ 123.29364557], [ 83.53840083], [ 64.67679778], [ 127.82433157], [ 11.3305656 ], [ 95.4101701 ], [ 126.53213908], [ 104.68868736], [ 32.45886112]]) In [5]: normal(100, 1000, 10) Out[5]: array([ 1052.93998938, -1254.12576419, 258.75390045, 688.32715327, -2.36543806, -1570.54842269, 472.90045029, 394.62908014, 137.10320437, 1741.85017871]) And just to exaggerate things a little more: In [6]: multivariate_normal([100], [[10000]], 10).T][0] Out[6]: array([ 274.45446694, 85.79359682, 245.03248721, 120.10912405, -34.76526896, 134.93446664, 47.6768889 , 93.34140984, 80.27244669, 229.64700591]) Whereas In [7]: normal(100, 10000, 10) Out[7]: array([ -554.68666687, 3724.59638363, -14873.55303901, -3111.22162495, -10813.66412901, 4688.81310356, -9510.92470735, -12689.02667559, -10379.01381925, -4534.60480031]) I'm shocked that I don't get some negative values in Out[4]. And Out[6] really ought to have some numbers in the thousands. I'd totally be willing to believe that I don't understand the multivariate normal and/or variance. Can someone tell me whether these numbers look sane? For the bivariate case I do something like this: means = [100, 100] variances = [100, 1000] Sx, Sy = variances sx, sy = map(sqrt, variances) cor = 0.7 cov = [[Sx, cor*sx*sy], [cor*sy*sx, Sy]] draws = 10 samples = multivariate_normal(means, cov, draws) As mentioned before, the samples are shockingly close to their means. Thanks, Josh