Kalman-and-Bayesian-Filters-in-Python
Kalman-and-Bayesian-Filters-in-Python copied to clipboard
rlabbe
BAD invocation of Central Limit Theorem
In Chapter 3, when first playing with the concept of a Gaussian, we have the following text:
What does this curve mean? Assume we have a thermometer which reads 22°C. No thermometer is perfectly accurate, and so we expect that each reading will be slightly off the actual value. However, a theorem called Central Limit Theorem states that if we make many measurements that the measurements will be normally distributed.
This is very wrong. The article which this excerpt links to describes CLT as the following:
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a bell curve) even if the original variables themselves are not normally distributed.
When you "make many measurements," if they are not normally distributed, then taking a lot of them will not magically make them normally distributed.
The only way to make them approximate a normal distribution is to take a number of them and average them (or just sum them together).
I'm sure this is well understood by the author, but the text as quoted is simply wrong.
