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2 marksRandom Variables

CAPE Applied Mathematics Unit 1 · 2013 · Paper 2 · Question 4(b)(i)

A continuous random variable X has a uniform probability density function f(x) = 1/5 from x = 1 to x = k.

Calculate the value of k.

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Other parts of this question

  1. 4(a)(i)Determine the value of a.[2 marks]
  2. 4(a)(ii)a)Calculate E[X].[3 marks]
  3. 4(a)(ii)b)Calculate Var[X].[3 marks]
  4. 4(a)(ii)c)Calculate P(X ≥ 2).[2 marks]
  5. 4(b)(ii)Show that P(X > 2) = 4/5.[2 marks]
  6. 4(c)(i)What is the probability that he sells exactly 3 defective tyres in the next 10 tyres of that brand?[3 marks]
  7. 4(c)(ii)The supplier expects a shipment of 500 tyres of that brand. How many of these tyres will be expected to be defective?[2 marks]
  8. 4(c)(iii)Using an approximate distribution, calculate an estimate for the probability that a shipment of 500 tyres will have more than 90 defective tyres.[6 marks]

More practice: the rest of this paper · more Random Variables questions · all CAPE Applied Mathematics Unit 1 past papers