Mathematics · Probability

Total Correlation Multi-Information sum of marginal entropies Solver

Rearrange the total correlation multi-information relationship and solve for sum of marginal entropies.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
sum of marginal entropies7.2
Reconstructed total correlation1.4

Calculation steps

  1. Use a=c+b with total correlation=1.4000000000000004 and joint entropy=5.8.
  2. sum of marginal entropies=7.2.
  3. Substitution into c=a−b reconstructs 1.4000000000000004.

Understand Total Correlation Multi-Information: solve sum of marginal entropies

One idea, three depths

Choose how deeply to explain Total Correlation Multi-Information: solve sum of marginal entropies

Total Correlation Multi-Information: solve sum of marginal entropies: Rearrange the total correlation multi-information relationship and solve for sum of marginal entropies.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Total Correlation Multi-Information: solve sum of marginal entropies to answer this question: rearrange the total correlation multi-information relationship and solve for sum of marginal entropies? Enter total correlation and joint entropy; the calculator shows sum of marginal entropies. For example: sum of marginal entropies=7.2 and joint entropy=5.8 produce total correlation=1.4000000000000004. The answer tells you sum of marginal entropies.

Age 15Explain it to a 15-year-oldConnect it to the formula

Total correlation subtracts joint entropy from the sum of all marginal entropies to measure multivariate dependence. This page isolates sum of marginal entropies and verifies it in the original relationship. The rule is a=c+b. Its input values are total correlation, joint entropy, and the main result is sum of marginal entropies. For example: sum of marginal entropies=7.2 and joint entropy=5.8 produce total correlation=1.4000000000000004.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated total correlation multi-information: solve sum of marginal entropies relation over the valid real-number domain stated below. The implemented relation is a=c+b, evaluated from total correlation, joint entropy to produce sum of marginal entropies. Total correlation subtracts joint entropy from the sum of all marginal entropies to measure multivariate dependence. This page isolates sum of marginal entropies and verifies it in the original relationship. All marginals and the joint distribution must use the same variables, probability model, and logarithm base.

Inputs and valid domain

  • total correlation must be a finite real number.
  • joint entropy must be a finite real number.

Important boundary: All marginals and the joint distribution must use the same variables, probability model, and logarithm base.

The formula

a=c+b

How the calculator works through it

It substitutes total correlation, joint entropy into the formula and exposes every numerical step above. The main output is sum of marginal entropies, accompanied by Reconstructed total correlation.

Read the result correctly

The sum of marginal entropies is the direct answer to “rearrange the total correlation multi-information relationship and solve for sum of marginal entropies.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

sum of marginal entropies=7.2 and joint entropy=5.8 produce total correlation=1.4000000000000004.

Where this model stops being reliable

All marginals and the joint distribution must use the same variables, probability model, and logarithm base.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Total Correlation Multi-Information: solve sum of marginal entropies works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Total Correlation Multi-Information: solve sum of marginal entropies uses a=c+b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

  • Probability as a modelled proportion

    Probability rules are needed to interpret what the Total Correlation Multi-Information: solve sum of marginal entropies result says about possible outcomes.

    Review this foundation about 5 min

Optional enrichment

  • Ordered arrangements

    Counting ordered arrangements can extend Total Correlation Multi-Information: solve sum of marginal entropies to more detailed sample spaces and event models.

    Review this foundation about 5 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read total correlation, joint entropy.
  2. Evaluate the principal relationship: a=c+b.
  3. Return sum of marginal entropies and check the domain conditions described above.
Python
            from math import *

def total_correlation_multi_information_solve_a(c, b) -> float:
    return (c + b)

assert abs(total_correlation_multi_information_solve_a(1.4000000000000004, 5.8) - 7.2) < 1e-6 * max(1.0, abs(7.2))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double total_correlation_multi_information_solve_a(double c, double b) {
    return (c + b);
}

int main(void) {
    const double expected = 7.2;
    const double actual = total_correlation_multi_information_solve_a(1.4000000000000004, 5.8);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double total_correlation_multi_information_solve_a(double c, double b) {
    return (c + b);
}

int main() {
    constexpr double expected = 7.2;
    const double actual = total_correlation_multi_information_solve_a(1.4000000000000004, 5.8);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double total_correlation_multi_information_solve_a(double c, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global total_correlation_multi_information_solve_a
section .text

total_correlation_multi_information_solve_a:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    addsd xmm0, [rbp-16]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = total_correlation_multi_information_solve_a(c, b)
    result = (c + b);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, b_] := (c + b);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Introductory Statistics 2e

Read the free OpenStax statistics textbook
Cite this book
APA 7
Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
MLA 9
Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
Chicago author-date
Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Total Correlation Multi-Information sum of marginal entropies Solver. MW SysArc Tools. https://math.mwsysarc.com/probability/total-correlation-multi-information-sum-of-marginal-entropies-solver

MLA 9

MW SysArc. “Total Correlation Multi-Information sum of marginal entropies Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/total-correlation-multi-information-sum-of-marginal-entropies-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Total Correlation Multi-Information sum of marginal entropies Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/total-correlation-multi-information-sum-of-marginal-entropies-solver.

Harvard

MW SysArc (2026) ‘Total Correlation Multi-Information sum of marginal entropies Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/total-correlation-multi-information-sum-of-marginal-entropies-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_total_correlation_multi_information_solve_a_2026,
  author = {{MW SysArc}},
  title = {Total Correlation Multi-Information sum of marginal entropies Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/probability/total-correlation-multi-information-sum-of-marginal-entropies-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Total Correlation Multi-Information sum of marginal entropies Solver
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/probability/total-correlation-multi-information-sum-of-marginal-entropies-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Total Correlation Multi-Information: solve sum of marginal entropies do?

Rearrange the total correlation multi-information relationship and solve for sum of marginal entropies.

How does the Total Correlation Multi-Information: solve sum of marginal entropies work?

The calculator applies a=c+b. Total correlation subtracts joint entropy from the sum of all marginal entropies to measure multivariate dependence. This page isolates sum of marginal entropies and verifies it in the original relationship.

What can I learn from the Total Correlation Multi-Information: solve sum of marginal entropies?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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