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4 marksContinuous Random Variables

CAPE Applied Mathematics Unit 2 · 2010 · Paper 2 · Question 3(a)(i)

The continuous random variable X has cumulative distribution function F(x) = 0 for x ≤ 3, k(x - 3) for 3 ≤ x ≤ 6, and 1 for x ≥ 6.

Calculate the value of the constant, k, and sketch the graph y = F(x).

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Other parts of this question

  1. 3(a)(ii)Calculate P(3.5 ≤ X ≤ 5).[3 marks]
  2. 3(a)(iii)Calculate the median of X.[3 marks]
  3. 3(a)(iv)Calculate the lower quartile of X.[4 marks]
  4. 3(b)(i)Determine the probability density function f(x) and sketch its graph.[4 marks]
  5. 3(b)(ii)Determine the expectation of X.[3 marks]
  6. 3(b)(iii)Determine the variance of X.[4 marks]

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