Law of Total Expectation

Industrial Engineering & Operations Research

Algebra
- Cheatsheet
- Logarithms
Linear Algebra
Real Analysis
- Sets
Calculus
- Calculus I
- Calculus II
- Calculus III
  - Vector-Valued Functions
- Integration
  - Rules
  - Leibniz's Rule
- Differential Equations
Geometry
- Cheatsheet
Probability Theory
Statistics
- Cheatsheet
- Descriptive Statistics
- Probability Distributions
- Functions
- Error Metrics
  - MD
  - MAE
  - MSE
  - RMSE
  - MPE
  - MAPE
  - R²
  - MSLE
  - Cross-Entropy Loss
- Hypothesis Testing
- Regression Analysis
- Correlation
- Non-Parametric Statistics
- Maximum Likelihood Estimation
- Generalized Linear Models
- Cross Validation
- Markov Chains
- Monte Carlo Simulation
- Design of Experiments
- Principal Component Analysis
- AIC & BIC
- Bootstrap & Resampling
- Types of Statistics
Time Series
- Moving Averages
- Decomposition
  - Classical
  - STL
- Frequency
  - Fourier
  - Periodogram
- Exponential Smoothing (ETS)
  - Summary
  - A-N-N
  - A-N-A
  - A-N-M
  - A-A-N
  - A-A-A
  - A-A-M
  - A-Ad-N
  - A-Ad-A
  - A-Ad-M
  - A-M-N
  - A-M-A
  - A-M-M
  - A-Md-N
  - A-Md-A
  - A-Md-M
  - M-N-N
  - M-N-A
  - M-N-M
  - M-A-N
  - M-A-A
  - M-A-M
  - M-Ad-N
  - M-Ad-A
  - M-Ad-M
  - M-M-N
  - M-M-A
  - M-M-M
  - M-Md-N
  - M-Md-A
  - M-Md-M
- ARIMA Family
  - Summary
  - AR
  - MA
  - ARMA
  - ARIMA
  - SARIMA
  - SARIMAX
  - VAR
  - VMA
  - VARMA
  - VARIMA
  - VARIMAX
System Dynamics
Operations Research
Supply Chain
- Planning
- Manufacturing
- Bullwhip Effect
- Classification
  - ABC
  - XYZ
  - ABC × XYZ
  - FSN
  - VED
- Metrics
- Service Levels
- Stocks
- Newsvendor
- Multi-Echelon
- Risk Pooling
- EOQ
- Policies
Graph Theory
- Overview
Machine Learning
- Bias–Variance Tradeoff
- Classification
  - Support Vector Machine
  - XGBoost
- Graphs
  - Graph Neural Network
Economics
Algorithms
- Dijkstra
Organisations
Certifications
- CSCP
- Supply Chain Analytics
- ACCA F3 — Financial Accounting
Appendix
- Scheduling Code
White Paper
References

148. Law of Total Expectation

Tower property
Law of iterated expectations
Smoothing theorem
Adam’s law

𝔼 [𝑋] = 𝔼 [𝔼 [𝑋 | 𝑌]]

← Mixture Distributions Law of Total Variance →