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3 marksContinuous Random Variables

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

A continuous random variable X has probability density function f(x) = k(4 - x) for 0 ≤ x ≤ 3, and 0 otherwise.

Determine the value of k.

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Other parts of this question

  1. 4(a)(i)State appropriate null and alternative hypotheses to test whether grades are uniformly distributed.[2 marks]
  2. 4(a)(ii)Determine the critical region for the chi-squared goodness-of-fit test at the 5% significance level.[3 marks]
  3. 4(a)(iii)Calculate the value of the chi-squared test statistic.[4 marks]
  4. 4(a)(iv)State a valid conclusion for the test, giving a reason.[2 marks]
  5. 4(b)(ii)Calculate P(X > 1).[3 marks]
  6. 4(b)(iii)Calculate the expected value E(X).[3 marks]
  7. 4(b)(iv)State fully the cumulative distribution function F(x).[3 marks]
  8. 4(b)(v)Hence, or otherwise, find P(1.5 < X < 2).[2 marks]

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