The Central Limit Theorem

Earlier in the chapter, when we were introducing specific continuous-valued distributions, we described the Gaussian or normal distribution and we said that it was an extremely important distribution because it was an extremely common distribution. By this, we meant that many datasets you will encounter will effectively have been drawn from a normal distribution, or you will use a normal distribution to model those datasets. We will now explain why.

Sums of random variables

Lots of the quantities we analyze as data scientists are aggregations of other data. Aggregating observations over some dimension to simplify the data is a very natural thing to do.

For example, consider our e-commerce scenario where we are interested in how many items are sold. The number of items sold on any day of the year we might model as a binomial random variable, but what about for the whole year? Imagine we have a relatively niche website where we only get, say, 20 visitors...