Why “probability of 0” does not mean “impossible” | Probabilities of probabilities, part 2

The video explores the concept of probabilities with a weighted coin, highlighting the paradox of assigning probabilities to continuous values. It introduces the idea of using probability density functions (PDFs) to resolve this paradox by focusing on ranges rather than individual values. The video also touches on measure theory and the use of integration in continuous probability settings.

What is the importance of ranges of values in the context of continuous probabilities?

How can we interpret the height of a bar in a probability density function?

How does the concept of probability change when moving from discrete to continuous settings?

What practical questions can be answered using the probability density function after observing outcomes?