4
8
16
256 2 The random variable \(T\) has an exponential distribution with mean 2 Find \(\mathrm { P } ( T \leq 1.4 )\)
Circle your answer.
\(\mathrm { e } ^ { - 2.8 }\)
\(\mathrm { e } ^ { - 0.7 }\)
\(1 - e ^ { - 0.7 }\)
\(1 - \mathrm { e } ^ { - 2.8 }\) The continuous random variable \(Y\) has cumulative distribution function $$\mathrm { F } ( y ) = \left\{ \begin{array} { l r } 0 & y < 2
- \frac { 1 } { 9 } y ^ { 2 } + \frac { 10 } { 9 } y - \frac { 16 } { 9 } & 2 \leq y < 5
1 & y \geq 5 \end{array} \right.$$ Find the median of \(Y\) Circle your answer. 2
\(\frac { 10 - 3 \sqrt { 2 } } { 2 }\)
\(\frac { 7 } { 2 }\)
\(\frac { 10 + 3 \sqrt { 2 } } { 2 }\) Turn over for the next question 4 Research has shown that the mean number of volcanic eruptions on Earth each day is 20 Sandra records 162 volcanic eruptions during a period of one week. Sandra claims that there has been an increase in the mean number of volcanic eruptions per week. Test Sandra's claim at the \(5 \%\) level of significance.