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IB Maths AI HL 4.14 – Linear Transformation of Variables Notes

IB Maths AI HL 4.14 – Linear Transformation of Variables Notes

Subject: Mathematics

Age range: 16+

Resource type: Worksheet/Activity

Last updated

15 April 2026

pdf, 404.1 KB
pdf, 404.1 KB
pdf, 417.93 KB
pdf, 417.93 KB

IB Maths AI HL 4.14 Notes – Linear Transformation of Variables

This IB Maths AI HL 4.14 resource covers Linear Transformations, Linear Combinations, and Unbiased Estimators and is fully aligned with the IB Applications and Interpretation HL syllabus

Students learn how expectation and variance change under linear transformations ( Y = aX + b ), including the key results ( E[Y] = aE[X] + b ) and ( {Var}(Y) = a^2 {Var}(X) ). The resource extends to linear combinations of multiple variables, highlighting when independence is required and how covariance affects variance.

The concept of unbiased estimators is developed, including why the sample mean is an unbiased estimator of ( \mu ) and why the sample variance (with ( n-1 )) is an unbiased estimator of ( \sigma^2 ).

Ideal for IB Maths AI HL teachers teaching expectation, variance, and statistical inference at an advanced level.

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