A-LevelMathematicsProbability and statistics9709/61 · May/June 2022 · Q48 Marks

The independent random variables X and Y have distributions Po(2) and B(20, ¹/₄) respectively.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[B1] E(Y) = 20 × ¹/₄ [= 5], Var(Y) = 20 × ¹/₄ × ³/₄ [= ¹⁵/₄ = 3.75] Both OE, SOI
[B1] Var(X) = 2 SOI or standard deviation = √2
[B1] E(X - 3Y) = 2 - 3 × 5 = -13
[M1] Var(X - 3Y) = 2 + 9 × '¹⁵/₄' [= 35.75] Correct formula using their values
[A1] Standard deviation of (X - 3Y) = 5.98 (3 s.f.) or √143/2 CWO
[M1] (0, 0) and (1, 15)
[M1] e⁻² × (2⁰/0!) × (²⁰C₀ × (¹/₄)⁰ × (³/₄)²⁰) + e⁻² × (2¹/1!) × (²⁰C₁₅ × (¹/₄)¹⁵ × (³/₄)⁵) Allow any λ. Poisson expressions must be seen
[A1] 0.000430 (3 sf) CWO (must have evidence of addition) Allow 0.00043 or 4.3(0) × 10⁻⁴

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, May/June 2022 Paper 6 Variant 1, question 4.

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