We don’t know what life will bring, but that’s why it’s so fun to view common everyday life events through a statistical lens.

For example, let’s suppose that I’m trying to estimate the time that I’ll end up waking up this upcoming Saturday; it’s important I can estimate this well in order to get things done with my day. The problem is that I don’t know exactly when I’ll wake up since, for example, I don’t fully know any of the following:

  • whether (or when) my cat will choose to run up the stairs and wail for attention
  • whether my cat will choose to jump on my face to try to wake me up
  • whether I'll have a terrifying nightmare that disrupts my sleep
  • whether loud thunder will strike right next to me
  • whether the sun will rise and bounce off of a poorly-placed mirror directly into my eyes
  • whether my alarm will bother me enough to force me to not hit the snooze button

The events on the above list may or may not have been chosen from experience.

Importantly, before we observe the time period from tonight to tomorrow morning, we don’t know what will transpire then, so mathematically, we can frame the events above as random events.

Upon closer inspection of the list, one could conclude that my cat is responsible for a fair bit of the random chaos, and perhaps, if I understood her thought processes more, I could better estimate how she’d act, quantify the probability of certain events taking place, take actions to eliminate some of the randomness (e.g., lock my door to prevent her feet from ever reaching my face), and in the end, form better predictions for when I’ll wake up. Likewise, I could also make similar statements about the other bullet points; I could learn more about nightmares and the climate, move my mirror, or use past alarm usage data to better understand the impact of each on my eventual wake.

I could never fully get rid of all of the randomness, though, as I can’t, for example, fully control the weather (or my cat) and know exactly how I’ll react to different stimuli on any particular instance.

In such a simple everyday example, we already have so much going on at once, and it’s not feasible to fully understand every single thing perfectly; in essence, life bombards us with things we are unsure about, and we have to make decisions every day in the face of imperfect knowledge.

Interestingly, these are prime situations for us to use the language of probability, statistics, and computer science to formalize what is going on, code up models and simulations to test certain intuitions, and squeeze out additional insights from doing so.

The following links describe a few cases that I personally found interesting to think about.

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