Probability & Statistics Essentials for Machine Learning
Chapter 1: Probability Foundations Revisited
Review of Sample Spaces and Events
Conditional Probability and Independence
Bayes' Theorem Explained
Introduction to Random Variables
Expected Value and Variance
Applying Probability Concepts in Python
Quiz for Chapter 1
Chapter 2: Common Probability Distributions
Bernoulli and Binomial Distributions
Poisson Distribution
Uniform Distribution
Normal (Gaussian) Distribution
Exponential Distribution
Properties and Use in Data Modeling
Working with Distributions in SciPy
Hands-on Practical: Simulating and Plotting Distributions
Quiz for Chapter 2
Chapter 3: Descriptive Statistics for Datasets
Measures of Central Tendency: Mean, Median, Mode
Measures of Dispersion: Variance, Standard Deviation, Range
Understanding Skewness and Kurtosis
Percentiles and Quartiles
Correlation Analysis
Distinguishing Correlation from Causation
Visualizing Data Summaries
Calculating Descriptive Stats with Pandas
Practice: Summarizing a Dataset
Quiz for Chapter 3
Chapter 4: Inferential Statistics: Sampling and Estimation
Populations and Samples
Overview of Sampling Methods
The Central Limit Theorem
Understanding Point Estimates
Confidence Intervals Explained
Calculating Confidence Intervals for Means
Hands-on Practical: Sampling Simulation and Interval Estimation
Quiz for Chapter 4
Chapter 5: Hypothesis Testing for Model Evaluation
Formulating Null and Alternative Hypotheses
Understanding Type I and Type II Errors
P-values Explained
Introduction to T-tests
Introduction to Chi-Squared Tests
Analysis of Variance (ANOVA) Overview
Performing Hypothesis Tests using Python
Practice: Applying T-tests to Sample Data
Quiz for Chapter 5
Chapter 6: Introduction to Regression Analysis
The Simple Linear Regression Model
Method of Least Squares Estimation
Interpreting Regression Coefficients
Model Evaluation Metrics (R-squared, MSE)
Assumptions of Linear Regression
Overview of Multiple Linear Regression
Building Regression Models with Python
Hands-on Practical: Fitting and Evaluating a Linear Model
Quiz for Chapter 6
Poisson Distribution
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- Introduction to Probability, Dimitri P. Bertsekas and John N. Tsitsiklis, 2008 (Athena Scientific) - A widely used and rigorous textbook for introductory probability, providing a detailed academic explanation of the Poisson distribution and its mathematical foundations.
- An Introduction to Statistical Learning with Applications in R, Gareth James, Daniela Witten, Trevor Hastie, Rob Tibshirani, 2013 (Springer) - This book provides a statistical learning perspective, offering context for how distributions like Poisson are used in modeling and discussing Poisson regression in a machine learning setting.
- Generalized Linear Models, P. McCullagh, J. A. Nelder, 1989 Vol. 37 (Chapman and Hall) DOI: 10.1201/9780203753736 - The authoritative reference for generalized linear models (GLMs), which include Poisson regression, a key application mentioned for modeling count data in the course section.