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6 marksContinuous Random Variables

CAPE Applied Mathematics Unit 2 · 2017 · Paper 2 · Question 3(b)(ii)

A continuous random variable X has probability density function f(x) = k for 1 \le x \le 5.

Determine E(X) and \operatorname{Var}(X).

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Other parts of this question

  1. 3(a)Find the probability that the 3 locals are on the committee.[5 marks]
  2. 3(b)(i)Calculate the value of the constant k and sketch the graph of f(x).[4 marks]
  3. 3(b)(iii)Calculate P(3 < X < 4.5).[3 marks]
  4. 3(b)(iv)Determine the cumulative distribution function, F(x) = P(X \le x), and sketch its graph.[4 marks]
  5. 3(b)(v)Calculate the median, m, of X.[3 marks]

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