The normal distribution | Probability and Statistics | NJ Wildberger

In this final lecture in this short introduction to Probability and Statistics, we introduce perhaps the most important probability distibution: the normal distribution, also known as the `bell-curve'. Its role is clarified by the Central Limit theorem, a key result in Statistics, that states roughly that if you sample an arbitrary probability distribution, discrete or continuous, then the averages of that sample end up resembling more and more a normal distribution as the number of terms in the sample increases.

Here we start with the standard normal, which has mean 0 and variance 1. Although we cannot compute probabilities directly with it, in the sense of evaluating integrals precisely, we can do so approximately. The Cumulative distribution function is a useful tool in helping us do this--essentially just the integral of the probability density function.

A general normal distribution is related to a standard normal via an affine transformation, and I explain how to go from one to another: the idea being that questions about a general normal distribution are usually converted to standard normal questions, and the answers converted back.

Thanks for watching the series!

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