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A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2021 · Q29 Marks

The diagram shows the graph of the probability density function, f, of a random variable X. [Figure 2.1]

  1. (a)Find the value of the constant k.[2]
  2. (b)Using this value of k, find f(x) for 0 ≤ x ≤ k and hence find E(X).[3]
  3. (c)Find the value of p such that P(p < X < 1) = 0.25.[4]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.

  1. [M1] 1/2 x k x k = 1
  2. [A1] k = 2
  3. [B1] f(x) = -1/2x + 1
  4. [M1] Attempt integration of xf(x) limits 0 to k. FT their f(x). Could be in terms of k.
  5. [A1] 2/3 or 0.667 (3 sf)
  6. [M1] ∫[p,1] (-1/2x+1)dx [= 0.25]
  7. [M1] (-x²/4 + x) from p to 1 = 0.25
  8. [M1] p² - 4p + 2 = 0
  9. [A1] p = 2 - √2 or 0.586

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.
Source
A-Level Mathematics, Feb/Mar 2021 Paper 6 Variant 2, question 2.

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