Bernoulli Distribution PMF
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Full Formula Properties
Category: Probability Theory
Baby Fast Definition
This formula gives the chance of getting a 1 or 0 in a single coin‑flip‑like experiment, using the coin's bias p.
The Bernoulli PMF tells us how likely a single yes‑or‑no experiment is to result in success (1) or failure (0). It combines a factor that rewards success with one that rewards failure, guaranteeing the probabilities always add up to 1 across the two possible outcomes.
Computes the probability of observing a specific outcome (0 or 1) in a Bernoulli trial
k∈{0,1}, p∈[0,1] (input: trial outcome and success probability; output: probability value)
Multiplies the success term p^{k} with the failure term (1-p)^{1-k}, linking outcome and probability
Changes with both k and p; probability shifts from p to 1‑p as the outcome flips
Can be visualized as the area of a rectangle whose side lengths are the two term values
The exponents always sum to 1 (k+(1‑k)=1), ensuring the expression stays a proper probability
If p→0, probability →0 for k=1 and →1 for k=0; if p→1, the opposite holds