The Bernoulli distributionJust the simplest of all distributions, a binary oracle: 1 or 0, success or failure, cat or not-a-cat. The great coin flip of statistical destiny. models a binary outcome: it returns 1 ("success") with probability p and 0 ("failure") with probability 1 - p.

Example:
Tossing a biased coin that lands heads with probability p = 0.7. Let "heads" be encoded as 1 and "tails" as 0.

Question:
What is the correct definition of the Bernoulli distribution?