| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Name the distribution |
| Difficulty | Easy -1.2 This is a straightforward multi-part question on discrete uniform distribution requiring only basic recall and routine calculations. Part (a) is direct recognition, parts (b)-(g) involve standard formulas for probability, cumulative distribution, expectation and variance, and part (h) uses simple linear transformation properties. No problem-solving or novel insight required—purely procedural application of well-rehearsed techniques. |
| Spec | 5.02e Discrete uniform distribution |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Mark |
| (a) | (Discrete) Uniform | B1 |
| (b) | \(P(X=4) = \frac{1}{5}\) oe | B1 |
| (c) | \(F(3) = \frac{3}{5}\) oe | B1 |
| (d) | \(P(3X-3 > X+4) = P(X > 3.5)\) | M1 |
| (d) | \(= \frac{2}{5}\) oe | A1 |
| (e) | \(E(X) = 3\) | B1 |
| (f) | \(E(X^2) = \frac{1}{5}(1^2+2^2+3^2+4^2+5^2)\) | M1 |
| (f) | \(= 11\) | A1 |
| (g) | \(\text{Var}(X) = 11 - 3^2\) or \(\frac{(5+1)(5-1)}{12}\) | M1 |
| (g) | \(= 2\) | A1 |
| (h) | \(11.4 = aE(X) - 3\) or \(11.4 = 3a-3\) | M1 |
| (h) | \(a = 4.8\) | A1 |
| (h) | \(\text{Var}(4.8X-3) = \text{'4.8'}^2 \times \text{'2'}\) | M1 |
| (h) | \(= 46.08\) awrt 46.1 | A1 |
## Question 3:
| Part | Answer/Working | Mark | Guidance |
|---|---|---|---|
| (a) | (Discrete) **Uniform** | B1 | For uniform |
| (b) | $P(X=4) = \frac{1}{5}$ oe | B1 | |
| (c) | $F(3) = \frac{3}{5}$ oe | B1 | |
| (d) | $P(3X-3 > X+4) = P(X > 3.5)$ | M1 | For identifying correct probabilities i.e. $P(X>3.5)$ or $P(X=4)+P(X=5)$ |
| (d) | $= \frac{2}{5}$ oe | A1 | |
| (e) | $E(X) = 3$ | B1 | |
| (f) | $E(X^2) = \frac{1}{5}(1^2+2^2+3^2+4^2+5^2)$ | M1 | For a correct expression |
| (f) | $= 11$ | A1 | |
| (g) | $\text{Var}(X) = 11 - 3^2$ or $\frac{(5+1)(5-1)}{12}$ | M1 | For either 'their (f)' $-$ 'their (e)'² or correct expression $\frac{(5+1)(5-1)}{12}$ |
| (g) | $= 2$ | A1 | |
| (h) | $11.4 = aE(X) - 3$ or $11.4 = 3a-3$ | M1 | Setting up correct linear equation using $aE(X)-3=11.4$ |
| (h) | $a = 4.8$ | A1 | May be implied by correct answer |
| (h) | $\text{Var}(4.8X-3) = \text{'4.8'}^2 \times \text{'2'}$ | M1 | For $a^2 \times \text{Var}(X)$ with values substituted; 'their Var$(X)$' $< 0$ is M0 |
| (h) | $= 46.08$ awrt **46.1** | A1 | |
---3. The discrete random variable $X$ has probability distribution
$$\mathrm { P } ( X = x ) = \frac { 1 } { 5 } \quad x = 1,2,3,4,5$$
\begin{enumerate}[label=(\alph*)]
\item Write down the name given to this distribution.
Find
\item $\mathrm { P } ( X = 4 )$
\item $\mathrm { F } ( 3 )$
\item $\mathrm { P } ( 3 X - 3 > X + 4 )$
\item Write down $\mathrm { E } ( X )$
\item Find $\mathrm { E } \left( X ^ { 2 } \right)$
\item Hence find $\operatorname { Var } ( X )$
Given that $\mathrm { E } ( a X - 3 ) = 11.4$
\item find $\operatorname { Var } ( a X - 3 )$\\
\includegraphics[max width=\textwidth, alt={}, center]{b7500cc1-caa6-4767-bb2e-e3d70474e805-09_2261_54_312_34}
$\_\_\_\_$ VAYV SIHI NI JIIIM ION OC\\
VJYV SIHI NI JIIIM ION OC\\
VJYV SIHI NI JLIYM ION OC
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2018 Q3 [14]}}