Mathematics: Analysis and Approaches · Topic 4: Statistics and probability

AHL4.14 — Variance and continuous random variables

Mathematics: Analysis and Approaches · SL / HL · syllabus-mapped notes

1. Variance of a discrete random variable

   Var(X) = E(X^2) - [E(X)]^2 and the standard deviation.

2. Continuous random variables and pdfs

   Probability density functions, area = probability, and the total-area condition.

3. Mode, median, mean and variance of a CRV

   Locating the mode and median, and integrating for E(X) and Var(X).

4. Linear transformations of X

   E(aX + b) = aE(X) + b and Var(aX + b) = a^2 Var(X).