5 The discrete random variable \(X\) has the following probability distribution function
$$\mathrm { P } ( X = x ) = \begin{cases} \frac { 1 } { n } & x = 1,2 , \ldots , n
0 & \text { otherwise } \end{cases}$$
5
- Prove that \(\mathrm { E } ( X ) = \frac { n + 1 } { 2 }\)
[0pt]
[3 marks]
5
- (ii) Prove that \(\operatorname { Var } ( X ) = \frac { n ^ { 2 } - 1 } { 12 }\)
| 5 | | State two conditions under which a discrete uniform distribution can be used to model the score when a cubic dice is rolled. | | [2 marks] |
|
| |