Questions — SPS SPS FM Statistics (26 questions)

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SPS SPS FM Statistics 2025 April Q7
9 marks Standard +0.3
The random variable \(y\) has probability density function f(y) given by $$f(y) = \begin{cases} ky(a - y) & 0 \leq y \leq 3 \\ 0 & \text{otherwise} \end{cases}$$ where \(k\) and \(a\) are positive constants.
    1. Explain why \(a \geq 3\) [1]
    2. Show that \(k = \frac{2}{9(a - 2)}\) [3]
Given that \(E(Y) = 1.75\)
  1. Find the values of a and k. [4]
  2. Write down the mode of Y [1]