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4 marksRandom Variables

CAPE Applied Mathematics Unit 1 · 2022 · Paper 2 · Question 3(c)(iv)

The continuous random variable X has probability density function f(x) = x/2 for 0 < x < 1, k for 1 <= x <= 2.5, and 0 otherwise.

Determine P(1/2 <= X <= 2).

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Other parts of this question

  1. 3(a)(i)If an individual is selected at random, find the probability of selecting a person who has primary education.[2 marks]
  2. 3(a)(ii)Find the probability of selecting a woman, given that she has tertiary education.[2 marks]
  3. 3(a)(iii)Find the probability of selecting a person with secondary education, given that the person is a male.[2 marks]
  4. 3(a)(iv)Determine if secondary education is independent of gender.[4 marks]
  5. 3(b)A company manufactures three brands of vehicles, A, B and C. The percentage of customers that purchases each of these vehicles is 35%, 50% and 15%…[3 marks]
  6. 3(c)(i)Calculate the value of k.[3 marks]
  7. 3(c)(ii)Sketch the graph of f(x).[3 marks]
  8. 3(c)(iii)Determine the upper quartile.[2 marks]

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