A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2020 · Q37 Marks

A random variable X takes values between 0 and 3 only and has probability density function as shown in the diagram, where c is a constant. [Figure X.X]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[B1] 1/2 x 3 x c = 1 (oe) and c = 2/3 shown
[M1] Allow M1 for 1/3 seen as a linear scale factor or Attempt to find equation of line (of form y = mx + c where c ≠ 0) and interval from 2 to 3 OE or Attempt to find the point (2, 2/9) using the equation of the line (of form y = mx +c where c ≠ 0) and then use area of triangle
[A1] 1/9 or 0.111(3sf)
[*M1] Equation of line is y = (-2/9)x + 2/3 (OE Must be of form y = mx + c (c ≠ 0))
[DM1] Attempt integration x × their f(x), ignore limits
[A1 FT] Correct integration and limits. FT their equation of line
[A1] = 1

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, Oct/Nov 2020 Paper 6 Variant 2, question 3.

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