(1.1) Intro to Probability Distributions

https://www.math.wm.edu/~leemis/chart/UDR/UDR.html

Modelling the Real World §

All models - financial models, weather models, machine learning models, make some assumptions/simplifications in order to unlock powerful analytical and predictive insights regarding the thing being modelled.

Heuristically, data science and modelling is all about simplifying the real world into some mathematical model.

For example, linear regression models the relationship between two variables by saying that one is just a linear function of the other, plus or minus a little bit of random error.

Probability is complicated, but it is just another tool used to simplify the much, much more complex real world.

Just think about how complex the real world actually is.

Take the innocent coin toss for example

What factors actually go into the outcome of that coin toss?

• The release angle
  • The release velocity
    • Any air current
      • The weight of the coin
        • The friction of the coin’s surface
          • The material it falls on
            • Some quantum physics, probably?
              • …

Instead, we simply package all of this randomness and cause-effect into a single, neat Bernoulli random variable, and simply say it is heads with probability 0.5, and tails with probability 0.5.

It is one of many ways to model some real-world event.

• Bernoulli trial
• Poisson process