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Foundationsfoundationconcept

Random Variables

Map uncertain outcomes to measurable numerical values.

Reviewed 2026-08-10TheQuantBateman ResearchReading note
01Intuition

Build the mental model first.

A random variable is a rule that assigns a number to each possible market outcome. The randomness is in the outcome, not in the rule.

ONE-LINE DEFINITION

Map uncertain outcomes to measurable numerical values.

02Mathematics

Now make it exact.

X:ΩR,FX(x)=P[Xx]X: \Omega \to \mathbb{R}, \quad F_X(x)=\mathbb{P}[X\le x]
Notation and units

Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.

03Assumptions

Every model has a price.

01

Educational conventions are stated explicitly and may simplify market quotation or settlement details.

02

Rates are continuously compounded unless the section says otherwise.

03

Inputs are deterministic in the base model.

“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
04Market use

Why a quant cares.

P&L distributions, payoff definitions, risk measures and simulation all start here.

IntuitionMathematicsImplementationDesk risk
05Desk view
FRONT OFFICE VIEW

The hedge has opinions.

Start with the quote convention, then ask which Foundations risk survives the hedge. A number without its convention is merely well-dressed ambiguity.

Ask Bateman about this model
06Related

Continue through the graph.