randn function does not work
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the average value of data generated by function 'randn' is not zero
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Walter Roberson
2017-11-27
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Any one call to randn() is a finite sampling of the infinite distribution. The mean of 0 is statistical, not guaranteed for any finite subset.
If it were otherwise, imagine doing randn(1,1): in order for the mean of that sampling to be 0 each randn(1,1) would have to return 0. For randn(1,2) with two values being generated, both would have to be 0 or the two would have to be exact negatives of each other.
You can do statistical modeling to figure out the probability of the mean of a finite sampling being more than any given value.
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Guillaume
2017-11-27
For some reason, my dice don't work either. I've thrown them many times, yet the mean value is not exactly 3.5.
>> mean(randn(1, 1e8))
ans =
-1.9019e-04
Pretty close to zero if you ask me. You'll only get exactly zero if you call randn an infinite number of times (or you're really lucky)
Binbin Zhang
2017-11-27
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David Goodmanson
2017-11-27
Somebody should mention that if you take N samples from a distribution with standard deviation 1, then the standard deviation of the N-sample mean is 1/sqrt(N). So in Guillaume's example with N = 1e8, you would expect an answer down around 1e-4, which is what happened.
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