What is a Stationary Random Process?

A stationary random process is like having a toy box that always gives you surprises, but the kind of surprises never change.

Imagine you have a bag full of marbles: red, blue, and green. Every time you reach in, you pull out one at random. Now, if this happens every day, and no matter when you do it, there’s always about the same number of each color, that's like a stationary random process, it keeps giving you surprises, but the way it works stays the same over time.

Think of your favorite clock. It ticks every second, and no matter what time of day or night it is, it always behaves the same way. A stationary random process is like that clock, it keeps going on forever, but it doesn’t get faster, slower, or change its pattern.

Even if you take out a marble and don't put it back, if the bag still has roughly the same number of each color, then it's still stationary. It might not be exactly the same every time, but it stays in the same kind of rhythm, just like your clock always ticks at the same rate.

So a stationary random process is something that keeps changing randomly, but its way of changing never changes over time.