| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2018 |
| Session | June |
| Topic | Moment generating functions |
| Type | Use MGF to find moments |
| Difficulty | Standard +0.3 This is a straightforward application of MGF properties requiring differentiation to find moments and using the MGF addition property for independent variables. The calculations are mechanical (differentiating $(1-2t)^{-3}$ and evaluating at t=0) with no conceptual challenges beyond standard Further Maths MGF theory, making it slightly easier than average. |
| Spec | 5.03d E(g(X)): general expectation formula |
3 The moment generating function of a random variable $X$ is $( 1 - 2 t ) ^ { - 3 }$.\\
(i) Find the mean and variance of $X$.\\
(ii) $X _ { 1 }$ and $X _ { 2 }$ are two independent observations of $X$. Find $\mathrm { E } \left[ \left( X _ { 1 } + X _ { 2 } \right) ^ { 3 } \right]$.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2018 Q3}}