Further Mathematics · Pearson Edexcel 9FM0 · Option FS2 · Topic 4

Combinations of random variables

Means and variances of sums and differences of independent normal random variables.

  • 1 sub-topic
  • Taught in Year 13
  • 19 practice questions
  • 1 animated lesson
Practice questions (19) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 4.1Combinations of random variablesY13

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Medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 19 questions in this topic, free, no account needed.

Combinations of random variables

Not needed for Year 12Medium

The variance of a combination · Year 13 · 1 mark

  1. XX and YY are independent, with Var⁡(X)=5\operatorname{Var}(X) = 5 and Var⁡(Y)=1\operatorname{Var}(Y) = 1. What is Var⁡(2X−3Y)\operatorname{Var}(2X - 3Y)?
    (1)

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  1. Var⁡(aX+bY)\operatorname{Var}(aX + bY)=a2Var⁡(X){}= a^2\operatorname{Var}(X)+b2Var⁡(Y){}+ b^2\operatorname{Var}(Y) for independent variables. Variances add, even for a difference.BB: 29

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Combinations of random variables

Not needed for Year 12Hard

Combinations of normal random variables · Year 13 · 5 marks

The masses of small parcels are A ~ N(15, 1.5²) grams and of large parcels B ~ N(40, 2.5²) grams, all independent.
  1. Find the probability that the total mass of three small parcels is greater than the mass of one large parcel.
    (5)
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  1. Define the difference and find P(D>0)\mathrm{P}(D > 0).D=A1+A2+A3−BD = A_1 + A_2 + A_3 - B
  2. E(D)=5\mathrm{E}(D) = 5
  3. Variances add, even for a difference.Var⁡(D)\operatorname{Var}(D)=3(1.52)+2.52{}= 3(1.5^2) + 2.5^2=13{}= 13
  4. P(D>0)=0.9172\mathrm{P}(D > 0) = 0.9172

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