Randomness is really important when we talk about probability. It affects a lot of different parts of this topic. Let’s break it down.

Basic Probability:

Events happen randomly. This randomness changes how likely something is to occur.

Probability Distributions:

These are ways to understand how likely different outcomes can be:

• Normal Distribution:
  This is shaped like a bell. Most of the data points are close to the average (mean), which we call ($\mu$). The spread of the data is measured using something called standard deviation ($\sigma$).

• Binomial Distribution:
  This tells us about the number of successful outcomes in a set number of tries, which we call $n$. The chance of success for each try is shown with the letter $p$.

• Poisson Distribution:
  This type is used for counting how many times something happens over a certain period. The average rate of events is called $\lambda$. This distribution shows how randomness affects these counts.

These distributions help us understand uncertainty and make predictions in data science. They allow us to make sense of random events and what might happen next.