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Random Variables · CAPE Applied Mathematics Unit 1

46 past-paper questions on Random Variables, part of Module 2: Managing Uncertainty, from every CAPE Applied Mathematics Unit 1 paper on Quelpr.

Practise Random Variables
  1. 3(d)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Show that X is a valid random variable.
  2. 3(d)(ii)5 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Calculate the mean and standard deviation of X.
  3. 3(d)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Calculate the value of k.
  4. 3(d)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Calculate the number of overtime hours that attendants will be expected to work each week.
  5. 3(d)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2Calculate the probability that an attendant will work less than 8 hours overtime in any week.
  6. 3(d)(i)4 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Construct the probability distribution table.
  7. 3(d)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Hence, determine P(X > 3).
  8. 3(d)(iii)5 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Calculate E(X) and Var(X).
  9. 3(c)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Determine the probability that the bakery will receive more than 6 orders on a given day.
  10. 3(c)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Calculate the mean number of orders for special cakes that the bakery will expect on any day.
  11. 4(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Determine the value of a.
  12. 4(a)(ii)a)3 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Calculate E[X].
  13. 4(a)(ii)b)3 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Calculate Var[X].
  14. 4(a)(ii)c)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Calculate P(X ≥ 2).
  15. 4(b)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Calculate the value of k.
  16. 4(b)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Show that P(X > 2) = 4/5.
  17. Q221 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1The continuous random variable X has a probability density function given by f(x) = \begin{cases} 0.5, & 0 < x < 2 \\ 0, & \text{otherwise} \end{cases} P\left(X < \frac{1}{2}\right) is
  18. Q251 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1Item 25 refers to the following information. The discrete random variable Y, where y takes on only the values 1, 2, 3 and 4, has a cumulative distribution function F(y) which is represented in the table…
  19. Q281 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1The random variable X has probability mass function P(X = x) for x = 3, 4, 5, 6 as shown below. \begin{array}{|l|c|c|c|c|} \hline x & 3 & 4 & 5 & 6 \\ \hline P(X = x) & a & 0.5 & 0.2 & 0.1 \\ \hline…
  20. Q181 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1P(-1 \le X \le 1) is
  21. Q221 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1The mean number of defective bulbs is
  22. Q231 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1The variance for the distribution of defective bulbs is
  23. Q241 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2015 · Paper 1The standard deviation of a discrete random variable, X, is
  24. 4(a)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Prepare a probability distribution table to show this information, giving values to 3 decimal places.
  25. 4(a)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Calculate P(2 <= X <= 4).
  26. 4(a)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Calculate the expected number of errors per page.
  27. Q221 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1A random variable X has the following probability distribution. \begin{tabular}{|l|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \\ \hline P(X = x) & 0.3 & 0.1 & 0.4 & 0.2 \\ \hline \end{tabular} P(X \ge 2) =
  28. Q281 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1The random variable, X, has a probability mass function P(X = x) for x = 3, 4, 5, 6 as shown in the following table. \begin{tabular}{|l|c|c|c|c|} \hline x & 3 & 4 & 5 & 6 \\ \hline P(X = x) & a & 0.5 & 0.2…
  29. 4(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2State, with reason, whether or not the given table represents a valid probability distribution.
  30. 4(a)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2State, with reason, whether or not the given table represents a valid probability distribution.
  31. 4(a)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2State, with reason, whether or not the given table represents a valid probability distribution.
  32. 4(b)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2Show that k = 1/7.
  33. 4(b)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2Determine P(4 ≤ X ≤ 6).
  34. 4(c)(i)6 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2Calculate Var(X).
  35. 4(c)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2Construct a cumulative distribution table for the random variable X.
  36. 4(c)(iii)1 mark· CAPE Applied Mathematics Unit 1 · 2016 · Paper 2Evaluate P(X ≥ 4).
  37. 3(c)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2Determine the value of p.
  38. 3(c)(ii)6 marks· CAPE Applied Mathematics Unit 1 · 2017 · Paper 2Calculate E(X) and Var(X).
  39. 3(b)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Calculate the value of the constant b.
  40. 3(b)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the expected value of X, E(X).
  41. 3(b)(iii)3 marks· CAPE Applied Mathematics Unit 1 · 2021 · Paper 2Determine the variance of X, Var(X).
  42. 3(c)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Calculate the value of k.
  43. 3(c)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Sketch the graph of f(x).
  44. 3(c)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Determine the upper quartile.
  45. 3(c)(iv)4 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Determine P(1/2 <= X <= 2).
  46. 4(b)(iv)4 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2If a repair time is exceptionally long, CompuFix pays compensation to the customer: US$250 if the repair time is between 50 and 55 hours. Determine the expected amount of compensation.

Related topics in Module 2: Managing Uncertainty