CAIE S2 2021 November — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2021
SessionNovember
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TopicContinuous Probability Distributions and Random Variables
4 A random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} \frac { 1 } { 18 } \left( 9 - x ^ { 2 } \right) & 0 \leqslant x \leqslant 3 \\ 0 & \text { otherwise } \end{cases}$$
  1. Find \(\mathrm { P } ( X < 1.2 )\).
  2. Find \(\mathrm { E } ( X )\).
    The median of \(X\) is \(m\).
  3. Show that \(m ^ { 3 } - 27 m + 27 = 0\).
4 A random variable $X$ has probability density function given by

$$f ( x ) = \begin{cases} \frac { 1 } { 18 } \left( 9 - x ^ { 2 } \right) & 0 \leqslant x \leqslant 3 \\ 0 & \text { otherwise } \end{cases}$$

(a) Find $\mathrm { P } ( X < 1.2 )$.\\

(b) Find $\mathrm { E } ( X )$.\\

The median of $X$ is $m$.\\
(c) Show that $m ^ { 3 } - 27 m + 27 = 0$.\\

\hfill \mbox{\textit{CAIE S2 2021 Q4}}
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