Probability and Statistics deals with randomness, data, and the methods we use to understand uncertainty and draw conclusions from observations.

Key Topics

• Combinatorics and Probability — Counting, sample spaces, and basic probability rules.
• Conditional Probability — Bayes' theorem: \(P(A|B) = \frac{P(B|A)\,P(A)}{P(B)}\).
• Random Variables — Discrete and continuous random variables, expected value, and variance.
• Common Distributions — Binomial, Poisson, normal (Gaussian), exponential, and uniform.
• Central Limit Theorem — The reason the normal distribution appears everywhere in nature.
• Statistical Inference — Confidence intervals, hypothesis testing, and p-values.
• Regression and Correlation — Modeling relationships between variables.
• Maximum Likelihood Estimation — Finding the parameters that make observed data most probable.

Why It Matters

Statistics is the science of data. It underpins medical research, quality control, polling, finance, artificial intelligence, and virtually every field that makes decisions based on evidence.