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Discrete Random Variables · CAPE Applied Mathematics Unit 2

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

Practise Discrete Random Variables
  1. 4(a)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Show that k = 1/10.
  2. 4(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Calculate E(X).
  3. 4(a)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Show that P(Y = 4) = 1/10.
  4. 4(a)(iv)6 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Tabulate all the possible values of Y with their corresponding probabilities.
  5. 4(a)(v)5 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Hence, or otherwise, calculate E(Y) and Var(Y).
  6. 4(a)(vi)2 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Determine E(3X + 2Y).
  7. 4(b)4 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2The random variable X has a Poisson distribution with mean 1.5. Calculate the probability that X is at least 2.
  8. 3(c)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Identify the distribution of X and state its parameter(s).
  9. 3(c)(ii)a)3 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Determine the probability that it takes EXACTLY 2 attempts to obtain a green ball.
  10. 3(c)(ii)b)3 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Determine the probability that it takes at LEAST 3 attempts to obtain the first green ball.
  11. 3(c)(ii)c)3 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Determine the probability that it takes LESS than 4 attempts to obtain the first green ball.
  12. 3(d)2 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Determine E(X).
  13. 4(a)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2On a particular stretch of road, there are on average 3 accidents per week. Find the probability that no accidents occur in a particular week.
  14. 4(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Find the probability that MORE than 3 accidents occur in a particular week.
  15. 4(a)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Find the probability that EXACTLY 6 accidents occur in a particular fortnight.
  16. 4(b)5 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2The probability that a student is awarded a pass in the statistics examination is 0.84. Find the probability that in a group of 12 students, MORE than two-thirds pass the statistics examination.
  17. 3(a)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine E(X + Y).
  18. 3(a)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine E(2X - 3Y).
  19. 3(a)(iii)4 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine \text{Var}(2X - 3Y).
  20. 3(b)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Calculate P(X \ge 3).
  21. 3(b)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Calculate E(X).
  22. 3(b)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Calculate P(X = 5).
  23. 4(a)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the probability of exactly 2 accidents in any one-week period.
  24. 4(a)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Given that on average 4 accidents occur in a 4-week period, show that the probability of at least 4 accidents in a 4-week period is 0.567 to 3 decimal places.
  25. 4(a)(iii)5 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2A year consists of approximately thirteen 4-week periods. Determine the probability that in a particular year there are exactly eleven periods during which AT LEAST 4 accidents occur.
  26. 4(b)6 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2With the use of another justified probability distribution function as an approximation, determine the probability that a box contains AT MOST two defective nails.
  27. 4(a)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Find the probability that there are EXACTLY 4 faults in a 15-metre length of cloth.
  28. 4(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Calculate the probability of AT LEAST 2 faults in a 60-metre length of cloth.
  29. 4(c)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Calculate P(X + Y = 3).
  30. 4(c)(ii)a)1 mark· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Evaluate E(X).
  31. 4(c)(ii)b)1 mark· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Evaluate Var(X).
  32. 4(c)(ii)c)1 mark· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Evaluate E(Y).
  33. 4(c)(ii)d)1 mark· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Evaluate Var(Y).
  34. 4(c)(iii)a)2 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Hence, determine E(3X – 2Y).
  35. 4(c)(iii)b)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Hence, determine Var(3X – 2Y).
  36. 3(a)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Determine the probability that in a random sample of 15 bolts, more than one is defective.
  37. 3(a)(ii)8 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2If X represents the number of defective bolts manufactured by the factory, determine the SMALLEST value of n for which the ratio of the standard deviation of X to the mean of X is less than 0.1.
  38. 3(b)5 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2If X ~ Bin(500, 0.005), use a suitable approximation to find P(X ≤ 2).
  39. 3(d)3 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2If X follows a geometric distribution with probability 0.3, determine the probability that X is less than 4.
  40. 2(a)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the probability that all three markers are red.
  41. 2(a)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the probability that exactly two of the markers are black.
  42. 2(c)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2In a random sample of 10 households, calculate the probability that exactly 6 have internet access.
  43. 2(c)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2In a random sample of 80 households, calculate the expected number that have internet access.
  44. 3(b)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the probability that a player starts the game on the third toss of the die.
  45. 3(b)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the probability that at most 5 tosses are necessary to start the game.
  46. 3(b)(iii)2 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Determine the expected number of tosses required to start the game.
  47. 3(c)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the probability that exactly 4 faulty reports are received on Monday.
  48. 3(c)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the probability that exactly 5 faulty reports are received over a five-day period.
  49. 4(a)4 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Determine, to 3 significant figures, the probability that a piece of metal 15\text{ m}^2 will contain at most three blisters.
  50. 4(b)5 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Justifying the use of a suitable approximation, calculate the probability that at least 2 customers intend to pay their arrears.
  51. 4(a)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Write a distribution, V, for the total mass of the 10 biscuits.
  52. 4(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Write a distribution, T, for the total mass of the package of biscuits.

Related topics in Module 2: Probability and Distributions