| Exam Board | AQA |
|---|
| Module | Further Paper 3 Statistics (Further Paper 3 Statistics) |
|---|
| Year | 2024 |
|---|
| Session | June |
|---|
| Topic | Continuous Probability Distributions and Random Variables |
|---|
| Type | Find expectation E(X) |
|---|
5 The continuous random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} \frac { 1 } { 6 } e ^ { \frac { x } { 3 } } & 0 \leq x \leq \ln 27
0 & \text { otherwise } \end{cases}$$
Show that the mean of \(X\) is \(\frac { 3 } { 2 } ( \ln 27 - 2 )\)