Probability theory

Interpretations of probability

Probability spaces

Events

Interpretation

Frequentist

Bayesian

Propensity

Determinist

Experiment

Bernoulli trial

Sample space of an experiment

σ-algebra of events

Event

Probability measure

Bayes theorem

Law of total probability

...

Sequence of events

Tail event

Zero-one law

Probability of tail events

First Borel–Cantelli lemma

Proof

Second Berel–Cantelli lemma

Proof

Example

Coin toss example Borel–Cantelli
Visualizing the sample space. (0, 0, 0, 0, 1, 0, 0, ...) Connecting definition with occurs infinitely many times.

Incomplete
Complete
2024-Jul-31 (46 hours ago)
2024-Jul-31 (46 hours ago)
2024-Jul-31 (46 hours ago)
2024-Jul-31 (46 hours ago)