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ZIMSEC A-Level Statistics

6.6Linear combinations of random variables

Linear combinations of random variables in ZIMSEC A-Level Statistics: what the syllabus expects you to know, the learning objectives and how to practise.
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Overview

Form 6.

Learning objectives

What the syllabus expects you to be able to do.

  1. 6.6.1Form 6: use E(aX ± b) = aE(X) ± b, Var(aX ± b) = a²Var(X), E(aX ± bY) = aE(X) ± bE(Y) and Var(aX ± bY) = a²Var(X) + b²Var(Y) for independent X and Y.
  2. 6.6.2Form 6: use the facts that linear combinations of independent normal variables are normal and sums of independent Poisson variables are Poisson.

Lessons

  • Linear combinations of random variables

    45 min

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Sample question

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Linear combinations of random variables: sample question

1 mark

E(X)=8\mathrm{E}(X) = 8 and Var(X)=3\mathrm{Var}(X) = 3. Find Var(5−2X)\mathrm{Var}(5 - 2X).

Only if the answer has a unit, e.g. cm or km/h.

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