Syllabus Map

AA HL Statistics & Probability Syllabus Points

The official IB syllabus content covering AHL points 4.13 through 4.15:

  1. 4.13Continuous random variables and their probability density functions (PDF) $f(x)$ with $\int_{-\infty}^\infty f(x)\,dx = 1$; cumulative distribution functions (CDF) $F(x) = P(X \le x) = \int_{-\infty}^x f(t)\,dt$
  2. 4.14Expected value (mean) $E(X) = \int x f(x)\,dx$, variance $\text{Var}(X) = E(X^2) - [E(X)]^2$, median ($F(m) = 0.5$), and mode for continuous probability distributions
  3. 4.15Linear combinations of random variables: $E(aX+b) = aE(X)+b$, $\text{Var}(aX+b) = a^2\text{Var}(X)$; for independent random variables $E(aX+bY) = aE(X)+bE(Y)$ and $\text{Var}(aX \pm bY) = a^2\text{Var}(X) + b^2\text{Var}(Y)$

Study by topic

AHL Topic 4 Interactive Study Guides

Equipped with our standard 4-tab interface: Study Notes, Practice Exercises (10 tiered problems with collapsible solutions), Formula Sheet, and Mini Test (MCQs & exam FRQs).

4.13 Continuous Random Variables & PDFs Definition and normalization condition of probability density functions, integrating to find probabilities $P(a \le X \le b)$, and establishing cumulative distribution functions (CDF). Open Interactive Guide 4.14, 4.15 Expectation, Variance & Linear Combinations Calculus methods for mean $E(X)$ and variance $\text{Var}(X)$, finding medians and modes, and algebraic variance and expectation rules for linear combinations $aX \pm bY$. Open Interactive Guide

Prerequisite Knowledge

Core SL Foundation Prerequisites

Review the 6 standard level Topic 4 guides:

4.1–4.2 Sampling & Data Displays 4.3 Mean, Variance & IQR 4.4 Correlation & Regression 4.5–4.6 Probability & Conditionals 4.7–4.8 Discrete Random Variables 4.9, 4.12 Normal Distribution & $Z$