Probability and Random Variables

10 algorithms in Financial Mathematics, Statistics, and Data Foundations · 10 with asserted arithmetic.

In this family#

1. Experiments, Outcomes, Sample Spaces, and Events verified

   Sizes a sample space and a candidate event, and checks that every outcome named in the event actually appears in the sample space.

   experimentsOutcomesSampleSpacesAndEvents(input)
2. Probability Rules, Complements, Unions, and Intersections verified

   Applies the complement and addition rules to a pair of events, deriving the probability that A does not happen and the probability that at least one of A or B happens.

   probabilityRulesComplementsUnionsAndIntersections(input)
3. Conditional Probability verified

   Rescales the joint probability of two events by each marginal in turn, giving the probability of A once B is known and the probability of B once A is known.

   conditionalProbability(input)
4. Independence and Dependence verified

   Compares the observed joint probability of two events against the product of their marginals, and reports both the verdict and the size of the gap.

   independenceAndDependence(input)
5. Bayes' Theorem and Base Rates verified

   Turns a prior, a true-positive rate, and a false-positive rate into the posterior probability of the condition given a positive result, along with the unconditional probability of that result.

   bayesTheoremAndBaseRates(input)
6. Discrete and Continuous Random Variables verified

   Validates a discrete random variable given as a support and a matching probability vector, echoing back the declared kind, the support, and the total mass it carries.

   discreteAndContinuousRandomVariables(input)
7. Expected Value verified

   Weights each value of a discrete random variable by its probability and sums the result, keeping the individual products so the total can be read term by term.

   expectedValue(input)
8. Variance, Moments, and Moment-Generating Intuition verified

   Computes the first two raw moments of a discrete random variable and derives its variance as the second raw moment less the square of the first.

   varianceMomentsAndMomentGeneratingIntuition(input)
9. Joint, Marginal, and Conditional Distributions verified

   Collapses a joint probability table over each axis in turn to give the two marginal distributions, then renormalises one slice of it to give the conditional distribution of X at a chosen value of Y.

   jointMarginalAndConditionalDistributions(input)
10. Covariance and Correlation of Random Variables verified

    Computes the probability-weighted covariance of the two variables in a joint distribution table and divides it by the product of their standard deviations to give the correlation.

    covarianceAndCorrelationOfRandomVariables(input)

What they share#

Every topic here is a record-transform, so once you have called one the rest follow the same shape. Import paths differ only in the final segment:

import { experimentsOutcomesSampleSpacesAndEvents } from "fintech-algorithms/foundations/probability-and-random-variables/experiments-outcomes-sample-spaces-and-events";
import { probabilityRulesComplementsUnionsAndIntersections } from "fintech-algorithms/foundations/probability-and-random-variables/probability-rules-complements-unions-and-intersections";

Read them in the order above — the sequence is pedagogical, not alphabetical.

Where this sits#

Financial Mathematics, Statistics, and Data Foundations collects 120 algorithms across 12 families. For the concept behind this family rather than the call signatures, see the concept guides.