Probability & Statistics Roadmap

From mathematical theory to practical data analysis for Data Science and Machine Learning.

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Phase Main Topic Content & Learning Activities Objectives & Deliverables
1. Foundations Mathematical Foundations & Set Theory
  • Calculus & Linear Algebra fundamentals.
  • Set Theory & Venn Diagrams.
  • Counting: Permutations, Combinations.
  • Build the necessary mathematical knowledge.
  • Solve basic counting problems.
2. Probability Core Basic Concepts of Probability
  • Sample Space, Events.
  • Definitions of Probability: Classical, Statistical.
  • Conditional Probability, Bayes' Theorem.
  • Delve into the first principles of probability theory.
  • Apply Bayes' theorem to solve problems.
3. Distributions Random Variables & Probability Distributions
  • Discrete & Continuous Random Variables.
  • Probability Density Function (PDF) & Cumulative Distribution Function (CDF).
  • Expectation, Variance, Standard Deviation.
  • Common Distributions: Binomial, Poisson, Normal.
  • Model the random outcomes of an experiment.
  • Calculate key metrics of distributions.
4. Multiple Variables Joint Probability Distributions
  • Joint & Marginal Distributions.
  • Covariance, Correlation Coefficient.
  • Central Limit Theorem (CLT).
  • Study the relationships between multiple random variables.
  • Understand the importance of the CLT.
5. Statistics Intro Introduction to Statistics
  • Descriptive Statistics: Mean, Median, Variance...
  • Data Visualization: Histograms, Box Plots.
  • Inferential Statistics: Population & Sample.
  • Begin the journey from theory to practical data analysis.
  • Summarize and visualize datasets.
6. Inference Parameter Estimation & Hypothesis Testing
  • Point Estimation: MLE Method.
  • Confidence Intervals for Mean & Proportion.
  • Hypothesis Testing: Null (H₀) & Alternative (Hₐ), p-value.
  • Common Tests: Z-test, t-test, Chi-squared.
  • Estimate population characteristics from sample data.
  • Use data to make decisions about claims.
7. Modeling Linear Regression
  • Simple & Multiple Linear Regression.
  • Ordinary Least Squares (OLS).
  • Model Evaluation: R-squared Coefficient.
  • Model the relationship between variables.
  • Build and evaluate simple predictive models.
8. Advanced & Applied Advanced Topics & Tools
  • Analysis of Variance (ANOVA).
  • Bayesian Statistics.
  • Markov Chains & Monte Carlo Simulation.
  • Applications in Data Science, Machine Learning, Finance.
  • Tools: Python (NumPy, Pandas, SciPy) & R.
  • Explore more specialized areas.
  • Apply knowledge to practice with real-world datasets.

Core Mindsets for Probability & Statistics

1. Embrace Uncertainty

The world is not deterministic. Learn to think in terms of probabilities and distributions, not just single outcomes. Statistics is the science of quantifying and managing uncertainty.

2. Data Tells a Story, with Context

Numbers are meaningless without context. Always seek to understand how the data was collected, what it represents, and what its limitations are before drawing conclusions.

3. Correlation is Not Causation

This is a fundamental rule. Just because two variables move together does not mean one causes the other. Always be skeptical and look for confounding factors.

4. Assumptions Matter

Every statistical test and model is built on a set of assumptions (e.g., normal distribution, independence). Understanding and verifying these assumptions is crucial for valid results.