the expectation value is simply 1e6 * P(1) = 1e6 * 1e6/2**32 = 232.83 ... the standard deviation is simply the square root of the expectation value, so 15.5.

Based upon a run of 100 samples, that seems to match quite nicely:

C:\test>bitvec2 -N=100
100
Mean: 230.95 stddev:14.75
[download]

I'm doing a run of 1000 samples, and if that shows no surprises, I'll be taking your figures as read and basing my testing upon it.

Thank you.

Update: The 1000 sample run marries well (good enough):

C:\test>bitvec2 -N=1000
1000
Mean: 233.39 stddev:15.79
[download]