6 The continuous random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} \frac { 1 } { 114 } ( 4 x + 7 ) & 0 \leq x \leq 6
0 & \text { otherwise } \end{cases}$$
6
- Show that the median of \(X\) is 3.87, correct to three significant figures.
[0pt]
[3 marks]
6 - Find the exact value of \(\mathrm { P } ( X > 2 )\)
| | 6 | | The continuous random variable \(Y\) has probability density function \(g ( y ) = \begin{cases} \frac { 1 } { 2 } y ^ { 2 } - \frac { 1 } { 6 } y ^ { 3 } | 1 \leq y \leq 3 | | 0 | \text { otherwise } \end{cases}\) | | " | 6- Show that \(\operatorname { Var } \left( \frac { 1 } { Y } \right) = \frac { 2 } { 81 }\)
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