Chapter 1
Literally chapter 1. So we all should have a general understanding or concept of Probabilities. It’s effectively a function that yields some value between 0 and 1. There are two types of probabilities: Discrete and Continuous. Let’s talk about these first.
Types of Probabilities
Discrete: When dealing with any data that is finite or countably infinite, that is considered discrete. This means anything that needs to be counted. Think about number of customers that sign up, or number of cars that pass by my house.
Continuous: Variables that are infinite are considered continuous. This mostly has to do with measurement. An example would be the amount of snow that falls. Did 3 inches fall, or 3.01? Or 3.001? Or 3.000001? etc.
Probability Density Function
When dealing with discrete variables, we can calculate probabilities by taking (# of successes)/(# of total outcomes). For example, what’s the probability of Heads on a fair coin? There are 2 outcomes, (Heads or Tails), and therefore, 1/2 is the probability.
However when dealing with continuous variables, it’s different. Take the snow example above. What’s the probability it will snow exactly 3 inches? Not 2.99 inches, or 3.01 inches, exactly 3? It’s pretty much 0 because it might snow close to 3 inches, but its extremely unlikely it will snow exactly 3.
This is where density functions come in. It’s basically a curve that describes some probability. You can’t read it like a normal plot though, because for any given value of x, the probability is 0. To get a probability from this, you measure an integral or area under the curve. In the snow example, we can measure the probability 2.99 to 3.01 inches which will be > 0. I’ll leave it there because I don’t feel like going into calculus. Just remember that area under the curve = probability with a pdf.
Summary
Discrete counts. Continuous measures. PDF’s aren’t a dumb file type that you can’t edit. Area under the curve. Pretty much what I took away from these sections. These are foundations for the next piece, which will go into Parametric Distributions. Specifically, the Binomial, Poisson, Normal, and Exponential Distributions. More to come.