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
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
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