| Exam Board | OCR |
|---|
| Module | Further Statistics (Further Statistics) |
|---|
| Year | 2018 |
|---|
| Session | March |
|---|
| Topic | Cumulative distribution functions |
|---|
| Type | Expectation from CDF/PDF |
|---|
2 A continuous random variable \(X\) has cumulative distribution function given by
$$\mathrm { F } ( x ) = \begin{cases} 1 - \frac { 1 } { x ^ { 3 } } & x \geqslant 1
0 & \text { otherwise } \end{cases}$$
Find \(E ( \sqrt { } X )\).