| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Name the distribution |
| Difficulty | Easy -1.3 This is a straightforward S1 question requiring only recognition of a discrete uniform distribution and application of standard linear transformation formulas for expectation and variance. Part (a) is pure recall, part (b) requires simple pattern recognition (R = 10Q + 4), and part (c) applies textbook formulas E(aQ+b) and Var(aQ+b) with no problem-solving required. |
| Spec | 5.02c Linear coding: effects on mean and variance5.02e Discrete uniform distribution |
| \(q\) | 1 | 2 | 3 | 4 | 5 |
| \(\mathrm { P } ( Q = q )\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) |
| \(r\) | 14 | 24 | 34 | 44 | 54 |
| \(\mathrm { P } ( R = r )\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Discrete Uniform | B1 | |
| (b) \(R = 10Q + 4\) | A2 | |
| (c) \(E(R) = (10 \times 3) + 4 = 34\) and \(\text{Var}(R) = 10^2 \times 2 = 200\) | M1 A1 | Total 7 marks |
**(a)** Discrete Uniform | B1 |
**(b)** $R = 10Q + 4$ | A2 |
**(c)** $E(R) = (10 \times 3) + 4 = 34$ and $\text{Var}(R) = 10^2 \times 2 = 200$ | M1 A1 | Total 7 marks
---2. The discrete random variable $Q$ has the following probability distribution.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$q$ & 1 & 2 & 3 & 4 & 5 \\
\hline
$\mathrm { P } ( Q = q )$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 5 }$ \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Write down the name of this distribution.
The discrete random variable $R$ has the following probability distribution.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$r$ & 14 & 24 & 34 & 44 & 54 \\
\hline
$\mathrm { P } ( R = r )$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 5 }$ & $\frac { 1 } { 5 }$ \\
\hline
\end{tabular}
\end{center}
\item State the relationship between $R$ and $Q$ in the form $R = a Q + b$.
Given that $\mathrm { E } ( Q ) = 3$ and $\operatorname { Var } ( Q ) = 2$,
\item find $\mathrm { E } ( R )$ and $\operatorname { Var } ( R )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [7]}}