Probability & Statistics: What You Actually Need to Know

The essential concepts learners use most in exams and analysis.

Introduction

Statistics becomes easy when you stop trying to memorize formulas and start understanding what questions are asking. Most exams and real-world analysis rely on a core set of ideas.

1) Probability Basics

• A probability is between 0 and 1

• Independent events: one doesn’t affect the other

• Conditional probability: probability changes with new information

2) Distributions (why they matter)

A distribution describes how values spread.

Know these:

• Normal distribution: common, symmetric, bell curve

• Binomial: number of successes in fixed trials

• Poisson: events occurring over time/space

3) Mean, Variance, Standard Deviation

• Mean: average

• Variance/SD: spread (how far from the mean)

Interpretation matters more than calculation.

4) Sampling and the Central Limit Theorem

Big idea: sample means tend to become normal as sample size grows.
This is why confidence intervals and hypothesis tests work.

5) Confidence Intervals (CI)

A CI gives a range likely to contain the true population value.

Translation: “We’re estimating with uncertainty.”

6) Hypothesis Testing (the exam favorite)

Key terms:

• Null hypothesis (H0): “no effect”

• Alternative (H1): “there is an effect”

• p-value: how surprising the result is under H0

• Significance level (α): threshold (often 0.05)

7) Correlation vs Regression

• Correlation: strength of relationship

• Regression: model relationship + predict

Important: correlation doesn’t prove causation.

Study method

1. Write what the question asks in plain language

2. Identify data type (continuous/discrete)

3. Choose tool (CI/test/regression)

4. Interpret result in words