Applications & Interpretation HL · Topic 4 · Statistics & Probability

IB Math AI HL Random Variables Worksheet (with full solutions)

Discrete and continuous random variables, expectation and variance, and linear combinations of random variables.

24 pages · 120 marks · with full solutions · free PDF for IB Mathematics: Applications and Interpretation HL students.

24pages
120marks
3difficulty levels
Yessolutions included
T4Statistics & Probability

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What this AI HL random variables worksheet covers

Discrete and continuous random variables, expectation and variance, and linear combinations of random variables. The questions follow the order of the AI HL syllabus for Topic 4 (Statistics & Probability) and are graded in three bands — routine practice, exam-standard, and the harder multi-step questions that separate a 6 from a 7.

Discrete distributions and E(X), Var(X)
Continuous pdfs and probabilities as integrals
E(aX + b) and Var(aX + b)
Linear combinations of independent normal variables
Exam tip for this topic. Variances add for independent variables even when you subtract them: Var(X − Y) = Var(X) + Var(Y).

Preview

How to use it

  1. Do the first band without the AI HL formula booklet, then check which formulas you had to look up — those are the ones to memorise.
  2. Time the second band at roughly 1.2 minutes per mark, the pace of Paper 1 and Paper 2.
  3. Mark the third band against the solutions and rewrite every question you lost marks on from a blank page.

More AI HL worksheets on Statistics & Probability

✓ = solutions included

Questions

Is this AI HL random variables worksheet free?

Yes — download the PDF with no sign-up. It is one of over 130 free IB Math worksheets on this site, written to match the current syllabus.

Does it come with answers?

Yes, full worked solutions are included at the end of the PDF.

Which IB course is it for?

IB Mathematics: Applications and Interpretation HL. The same topic is also available for the other courses where it is on the syllabus — see the links above.

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