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3 marksDiscrete Random Variables

CAPE Applied Mathematics Unit 2 · 2014 · Paper 2 · Question 4(a)(i)

Faults occur randomly in a cloth production process at a rate of 3 every 15 metres.

Find the probability that there are EXACTLY 4 faults in a 15-metre length of cloth.

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Other parts of this question

  1. 4(a)(ii)Calculate the probability of AT LEAST 2 faults in a 60-metre length of cloth.[3 marks]
  2. 4(b)(i)Calculate the probability that the mass is less than 60 g.[4 marks]
  3. 4(b)(ii)Calculate the probability that the mass is between 61 g and 64 g.[4 marks]
  4. 4(c)(i)Calculate P(X + Y = 3).[2 marks]
  5. 4(c)(ii)a)Evaluate E(X).[1 mark]
  6. 4(c)(ii)b)Evaluate Var(X).[1 mark]
  7. 4(c)(ii)c)Evaluate E(Y).[1 mark]
  8. 4(c)(ii)d)Evaluate Var(Y).[1 mark]
  9. 4(c)(iii)a)Hence, determine E(3X – 2Y).[2 marks]
  10. 4(c)(iii)b)Hence, determine Var(3X – 2Y).[3 marks]

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