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2 marksDiscrete Random Variables

CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2 · Question 4(a)(i)

The discrete random variable X has probability density function P(X = x) = kx for x = 1, 2, 3, 4, and 0 otherwise.

Show that k = 1/10.

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Other parts of this question

  1. 4(a)(ii)Calculate E(X).[3 marks]
  2. 4(a)(iii)Show that P(Y = 4) = 1/10.[3 marks]
  3. 4(a)(iv)Tabulate all the possible values of Y with their corresponding probabilities.[6 marks]
  4. 4(a)(v)Hence, or otherwise, calculate E(Y) and Var(Y).[5 marks]
  5. 4(a)(vi)Determine E(3X + 2Y).[2 marks]
  6. 4(b)The random variable X has a Poisson distribution with mean 1.5. Calculate the probability that X is at least 2.[4 marks]

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