The saga of theorems Central Limit Theorem
It's astonishing, but chance is governed by a law! The normal distribution is ubiquitous in mathematics and more generally in all sciences. How Gauss sensed it through astronomy and Laplace through extension of the binomial distribution? What makes it so powerful? What role does the central limit theorem play in this adventure? Opinion polls are an application of this result, but their reliability must be taken with a grain of salt, as errors are due to the choice of samples and the methods used.
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Can opinion polls be trusted?
How are opinion polls conducted? What mathematical theory underpins them? What biases affect them? A survey of surveys...
The central limit theorem and the laws of large numbers: so many laws!
One might expect the many independent causes behind a phenomenon to generate chaos (in the everyday, not the mathematical, sense). Nothing could be further from the truth—quite the opposite! The extreme regularity of complex phenomena has been proved to varying degrees...
The ubiquitous normal distribution
Is it not astonishing that chance should obey a law? Two of the greatest mathematical geniuses proved that most random phenomena are governed by the "normal" distribution. Simple in form, it underpins the statistical interpretation of a set of measurements.