| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discrete Probability Distributions |
| Type | Calculate E(X) from given distribution |
| Difficulty | Easy -1.8 This is a straightforward textbook exercise requiring only direct application of standard formulas for E(X), Var(X), and linear transformations. No problem-solving insight needed—just arithmetic computation of ΣrP(r) and Σr²P(r), then applying E(aX+b) and SD(aX+b) rules. Significantly easier than average A-level questions. |
| Spec | 5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
| \(r\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| \(\mathrm { P } ( \mathrm { X } = \mathrm { r } )\) | 0.05 | 0.1 | 0.25 | 0.3 | 0.15 | 0.1 | 0.05 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | E(X) = 2.9 |
| Var(X) = 2.09 | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (b) | Mean = £2450 |
| Answer | Marks |
|---|---|
| Standard deviation = £723 [£722.84] | B1FT |
| Answer | Marks |
|---|---|
| [3] | 3.3 |
| Answer | Marks |
|---|---|
| 1.1 | For 5002×𝑡ℎ𝑒𝑖𝑟 variance Do not allow M1 for use of 2.9 |
Question 1:
1 | (a) | E(X) = 2.9
Var(X) = 2.09 | B1
B1
[2] | 1.1
1.1
1 | (b) | Mean = £2450
Variance of salary = 5002×2.09 (= 522500)
Standard deviation = £723 [£722.84] | B1FT
M1
A1FT
[3] | 3.3
1.1
1.1 | For 5002×𝑡ℎ𝑒𝑖𝑟 variance Do not allow M1 for use of 2.9
unless stated to be Var(X). Do not allow M1 for simply
5002×Var(𝑋) without substituting in a value for Var(X)
Allow 722.8. Do not allow to greater accuracy than the
nearest penny. Do not allow answer given only in surds.1 The number of insurance policy sales made per month by a salesperson is modelled by the random variable $X$, with probability distribution shown in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | }
\hline
$r$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
$\mathrm { P } ( \mathrm { X } = \mathrm { r } )$ & 0.05 & 0.1 & 0.25 & 0.3 & 0.15 & 0.1 & 0.05 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find each of the following.
\begin{itemize}
\item $\mathrm { E } ( X )$
\item $\operatorname { Var } ( X )$
\end{itemize}
The salesperson is paid a basic salary of $\pounds 1000$ per month plus $\pounds 500$ for each policy that is sold.
\item Find the mean and standard deviation of the salesperson's monthly salary.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2024 Q1 [5]}}