| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2003 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Two or more different variables |
| Difficulty | Moderate -0.5 This is a straightforward application of standard results for linear combinations of independent normal variables. Students need to recall that E(X-Y) = E(X) - E(Y) and Var(X-Y) = Var(X) + Var(Y), then perform a routine normal probability calculation. All three parts are direct applications of learned formulas with no problem-solving or insight required, making it slightly easier than average. |
| Spec | 5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
3. Given the random variables $X \sim \mathrm {~N} ( 20,5 )$ and $Y \sim \mathrm {~N} ( 10,4 )$ where $X$ and $Y$ are independent, find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { E } ( X - Y )$,
\item $\operatorname { Var } ( X - Y )$,
\item $\mathrm { P } ( 13 < X - Y < 16 )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2003 Q3 [9]}}