What is Time-Invariant vs. Time-Varying?

Time-invariant means something stays the same over time, while time-varying means it changes as time goes on.

Imagine you're playing with a toy train that runs around a track. If the train always takes 5 minutes to go all the way around, no matter what, that’s time-invariant. It's like your favorite song that never changes, same notes, same beat every time you listen to it.

But if sometimes the train goes fast and sometimes slow, so it might take 3 minutes or 7 minutes to finish a lap, that’s time-varying. It’s like when you’re eating candy, you always finish your candy in the same amount of time, but when you're playing with your brother, you might take longer because you're distracted.

Think about your bedtime. If you go to bed at 8 PM every night and wake up at 7 AM every morning, that’s time-invariant, like a clock ticking the same each day.

But if sometimes you stay up late watching cartoons, or sleep in because it's the weekend, then your bedtime is time-varying. It changes depending on what happens!