확률

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A herbarium of probability — pressed concepts, hand-bound, slightly faded.

概念의 庭園

Garden of concepts — six pressed leaves, six theorems

정규분포

Normal distribution — bell of stillness

f(x) = (1/σ√2π) · e-(x-μ)²/2σ²

이항분포

Binomial — repeated coins, counted

P(k) = (n,k) pk (1-p)n-k

베르누이

Bernoulli — a single coin in dim light

P(X=1) = p, P(X=0) = 1-p

포아송

Poisson — rare arrivals, gentle clatter

P(k) = (λke) / k!

조건부확률

Conditional — what if, what given

P(A|B) = P(A∩B) / P(B)

베이즈정리

Bayes — what we know, updated

P(H|E) = P(E|H)P(H) / P(E)

枝의 길

Branching paths — chance unfolds, root to tip

Two consecutive days of weather, drawn as ink on rice paper. The thicker the branch, the more often this path is taken.

分布의 帳

Field-journal of common distributions

Name · 이름
Support
Mean · μ
Variance · σ²
Bernoulli · 베르누이
{0, 1}
p
p(1-p)
Binomial · 이항
{0, 1, …, n}
np
np(1-p)
Poisson · 포아송
{0, 1, 2, …}
λ
λ
Uniform · 균등
[a, b]
(a+b)/2
(b-a)²/12
Normal · 정규
(-∞, ∞)
μ
σ²
Exponential · 지수
[0, ∞)
1/λ
1/λ²

— annotated by an unhurried hand, in fading ink —