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Continuous Random Variables · CAPE Applied Mathematics Unit 2

37 past-paper questions on Continuous Random Variables, part of Module 2: Probability and Distributions, from every CAPE Applied Mathematics Unit 2 paper on Quelpr.

Practise Continuous Random Variables
  1. 3(a)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Calculate the value of the constant, k, and sketch the graph y = F(x).
  2. 3(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Calculate P(3.5 ≤ X ≤ 5).
  3. 3(a)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Calculate the median of X.
  4. 3(a)(iv)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Calculate the lower quartile of X.
  5. 3(b)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Determine the probability density function f(x) and sketch its graph.
  6. 3(b)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Determine the expectation of X.
  7. 3(b)(iii)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Determine the variance of X.
  8. 4(a)(i)6 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Determine the standard deviation of the length of wood cut.
  9. 4(a)(ii)5 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Determine the proportion of the pieces that are longer than 3.2 metres.
  10. 3(c)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Calculate, to 3 decimal places, P(X \ge 65).
  11. 3(c)(ii)5 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Calculate, to 3 decimal places, P(40 \le X \le 80).
  12. 4(c)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the value of the constant k.
  13. 4(c)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the value of t such that P(X > t) = \frac{1}{4}.
  14. 4(b)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Calculate the probability that the mass is less than 60 g.
  15. 4(b)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Calculate the probability that the mass is between 61 g and 64 g.
  16. 3(c)5 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2If X ~ Po(20), use a suitable approximation to find P(X ≤ 25).
  17. 4(a)(i)10 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Show that a = 2.2 and determine the value of b.
  18. 4(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Determine P(X > 0.5).
  19. 2(b)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Find the probability that a randomly chosen customer spends more than 8 minutes completing a transaction.
  20. 2(b)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Find the time below which 80% of customers spend completing a transaction.
  21. 4(b)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Determine the value of k.
  22. 4(b)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate P(X > 1).
  23. 4(b)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the expected value E(X).
  24. 4(b)(iv)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2State fully the cumulative distribution function F(x).
  25. 4(b)(v)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Hence, or otherwise, find P(1.5 < X < 2).
  26. 3(b)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Calculate the value of the constant k and sketch the graph of f(x).
  27. 3(b)(ii)6 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Determine E(X) and \operatorname{Var}(X).
  28. 3(b)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Calculate P(3 < X < 4.5).
  29. 3(b)(iv)4 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Determine the cumulative distribution function, F(x) = P(X \le x), and sketch its graph.
  30. 3(b)(v)3 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Calculate the median, m, of X.
  31. 4(c)(i)1 mark· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2State clearly the distribution which can be used to approximate the Poisson distribution.
  32. 4(c)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Calculate the probability that in one hour less than 32 calls are received.
  33. 4(c)(iii)4 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Calculate the probability that in one hour between 31 and 39 calls are received.
  34. 3(c)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Show that k = 1/9.
  35. 3(c)(ii)6 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Calculate E(X) and Var(X).
  36. 3(c)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Calculate P(X > 2).
  37. 4(a)(iii)8 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Calculate the probability that the total mass of the package of biscuits is less than 510 g.

Related topics in Module 2: Probability and Distributions