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3 marksRandom Variables

CAPE Applied Mathematics Unit 1 · 2016 · Paper 2 · Question 4(b)(ii)

A continuous random variable X has a trapezoidal probability density function f(x) from 0 to 10 with peak height k between 2 and 6.

Determine P(4 ≤ X ≤ 6).

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Other parts of this question

  1. 4(a)(i)State, with reason, whether or not the given table represents a valid probability distribution.[2 marks]
  2. 4(a)(ii)State, with reason, whether or not the given table represents a valid probability distribution.[2 marks]
  3. 4(a)(iii)State, with reason, whether or not the given table represents a valid probability distribution.[2 marks]
  4. 4(b)(i)Show that k = 1/7.[2 marks]
  5. 4(c)(i)Calculate Var(X).[6 marks]
  6. 4(c)(ii)Construct a cumulative distribution table for the random variable X.[2 marks]
  7. 4(c)(iii)Evaluate P(X ≥ 4).[1 mark]
  8. 4(d)(i)If 80 persons are introduced to the product, determine the number of persons who are expected to buy the product.[2 marks]
  9. 4(d)(ii)From a random sample of 15 persons who were introduced to the product, calculate the probability that exactly 9 will buy the product.[3 marks]

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