19.5 Summary
With the introduction of random variables, we learned to represent abstract probability spaces as random variables, mapping a sufficiently expressive collection of events to the real numbers. Instead of σ-algebras and probability measures, now we can deal with numbers. As I told you, “The strength or probability lies in its ability to translate real-world phenomena into coin tosses, dice rolls, dart throws, lightbulb lifespans, and many more.”
Most common random variables come in two forms: discrete or continuous, meaning that either it can be described with a probability mass function
or with a density function fX, satisfying
Translating experiments to distributions is the secret sauce of probability theory and statistics. For instance, the time between call center calls, bus arrivals, earthquakes, and insurance claims are all modeled with the exponential distribution, a mathematical object we can work with.
I know that learning takes a lifetime...
