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3 marksContinuous Random Variables

CAPE Applied Mathematics Unit 2 · 2018 · Paper 2 · Question 3(c)(i)

A continuous random variable, X, has probability density function f(x) = kx^2 for 0 < x < 3.

Show that k = 1/9.

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Other parts of this question

  1. 3(a)(i)Determine the number of ways in which this can be done if there are no restrictions.[2 marks]
  2. 3(a)(ii)Determine the number of ways in which this can be done if exactly 2 women must be chosen.[3 marks]
  3. 3(a)(iii)Calculate the probability that the chosen committee will include exactly 2 women.[2 marks]
  4. 3(b)(i)In how many ways can 3 jobs be assigned to the 5 teams if any team can be assigned only one job?[2 marks]
  5. 3(b)(ii)In how many ways can the jobs be assigned so that Team M is given the first job?[2 marks]
  6. 3(b)(iii)What is the probability that Team M gets the first job?[2 marks]
  7. 3(c)(ii)Calculate E(X) and Var(X).[6 marks]
  8. 3(c)(iii)Calculate P(X > 2).[3 marks]

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