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