In this first part of the week's work, we are going to switch gears to start building out statistical, rather than pure mathematical reasoning.
At this point, we begin to ask (and hopefully answer!) questions like:
- If we know that the math works when it is pure, then what guarantees can we get when we do the dirty work of dealing with data?
- What sorts of processes lead data to be distributed in particular ways?
- And, why is it distributed in these ways?
To be specific, you will learn:
- About statistics (which are just functions applied to data) and properties that you might want your statistics to possess in order to be useful.
- The Weak Law of Large Numbers, which states that under general conditions the sample mean converges in probability to the expected value of a random variable.
This begins what some people might recognize as core statistics work.