Data Science and Machine Learning (Theory and Projects) A to Z - Probability Model: Probability Models Continuous

The video tutorial explains the difference between discrete and continuous probability models. Discrete models have countable sample spaces, allowing positive probabilities for single outcomes. In contrast, continuous models have uncountable sample spaces, making it impossible to assign positive probabilities to single elements due to the additivity axiom. An example using a dart game on a unit circle illustrates this concept. The video concludes by highlighting the need to assign probabilities to intervals in continuous models and previews the next topic on conditional probabilities.

What is the additivity axiom of probabilities and how does it relate to assigning probabilities in continuous models?

How do probabilities get assigned to intervals rather than single elements in continuous probability models?

Summarize the key distinctions between discrete and continuous probability models.