The study of chance. The mathematics of maybe.
The Distribution
Every outcome lies somewhere on the curve. Some cluster at the center — the expected, the likely, the probable. Others drift to the tails, improbable but never impossible.
The distribution does not judge. It simply describes the shape of possibility, the topology of chance. Where are you most likely to be found?
P(x) = (1/σ√2π) e-(x-μ)²/2σ²
The Variables
Independence 독립
Two events, each ignorant of the other. The outcome of one changes nothing about the outcome of its neighbor. True independence is rare — in probability and in life.
P(A ∩ B) = P(A) · P(B)Conditional 조건
Given what you already know, how does the landscape shift? Conditional probability is the mathematics of context — every new observation redraws the curve.
P(A|B) = P(A ∩ B) / P(B)Expected Value 기대값
The center of gravity. If you repeated the experiment infinitely, the average outcome converges here. Not a prediction — a gravitational truth.
E[X] = Σ xi · P(xi)As samples grow infinite, randomness resolves into pattern.
The law of large numbers is not a law of mathematics alone —
it is the quiet promise that understanding emerges from observation.