Kalman-and-Bayesian-Filters-in-Python
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rlabbe
Remark on Central Limit Theorem in Chapter 3
In Chapter 3 on Gaussians, you wrote:
However, a theorem called Central Limit Theorem states that if we make many measurements that the measurements will be normally distributed.
This is not correct. The Central Limit Theorem states that the i.i.d. sample mean (i.e., take many independent samples from a random variable of any distribution and take its mean) will be normally distributed in the limit that the number of samples goes to infinity.
A suggestion is that your narrative should say something like:
a physical measurement process tend to combine many independent random variables such that the values of these measurements tend to appear to be normally distributed (i.e., Gaussians are a good model) by the Central Limit Theorem.
I have got stuck at this particular claim just recently, while reading the notebook (which, by the way, was a great help so far to me) and could not wrap my head around it.
@aichao I do not think that even what you propose is either obvious (to claim) or what @rlabbe wanted or needed to say.
The claim (as I understand it) is about the type of PDF for sensor measurement, and does not really depend on the number of measurements, unless it is an inherent feature of the sensor itself, e.g. it does internally some sampling and averaging, but this is definitely not obvious either from the text, or from the CLT.
