| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2006 |
| Session | January |
| 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. Parts (a) and (b) require direct recall of E(X+Y) = E(X) + E(Y) and Var(X+Y) = Var(X) + Var(Y), while part (c) involves routine standardization and normal table lookup. No problem-solving or conceptual insight is needed beyond applying memorized formulas. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.04a Linear combinations: E(aX+bY), Var(aX+bY)5.04b Linear combinations: of normal distributions |
2. A workshop makes two types of electrical resistor.
The resistance, $X$ ohms, of resistors of Type A is such that $X \sim \mathrm {~N} ( 20,4 )$.\\
The resistance, $Y$ ohms, of resistors of Type B is such that $Y \sim \mathrm {~N} ( 10,0.84 )$.\\
When a resistor of each type is connected into a circuit, the resistance $R$ ohms of the circuit is given by $R = X + Y$ where $X$ and $Y$ are independent.
Find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { E } ( R )$,
\item $\operatorname { Var } ( R )$,
\item $\mathrm { P } ( 28.9 < R < 32.64 )$\\
(6)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2006 Q2 [9]}}