| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2020 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Variance of linear transformation |
| Difficulty | Easy -1.2 This is a straightforward application of discrete uniform distribution properties and linear transformation rules. All parts require direct recall of formulas: stating X~DU(1,8), calculating a simple probability (3/8), applying standard E(X) and Var(X) formulas for uniform distributions, then using E(aX+b) and Var(aX+b) transformation rules. No problem-solving or novel insight required—purely routine calculations well below average A-level difficulty. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.02e Discrete uniform distribution |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | Uniform |
| On the values {1, 2, …, 8} | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.2 | For uniform |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | P(X < 4) = 0.375 |
| [1] | 1.1 | |
| 4 | (c) | E(X) = 4.5 |
| Answer | Marks |
|---|---|
| 64−1 21 | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (d) | 12 = 4 |
| Answer | Marks |
|---|---|
| 10 × 4 | B1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | FT their Var(X) from (c) |
Question 4:
4 | (a) | Uniform
On the values {1, 2, …, 8} | B1
B1
[2] | 3.3
1.2 | For uniform
For values
4 | (b) | P(X < 4) = 0.375 | B1
[1] | 1.1
4 | (c) | E(X) = 4.5
Var(X) =
64−1 21 | B1
B1
[2] | 1.1
1.1
4 | (d) | 12 = 4
E(Y) = 50
Var(Y) =
= 5252 2 1
10 × 4 | B1
M1
A1
[3] | 1.1
1.1a
1.1 | FT their Var(X) from (c)4 A fair 8 -sided dice has faces labelled $1,2 , \ldots , 8$. The random variable $X$ represents the score when the dice is rolled once.
\begin{enumerate}[label=(\alph*)]
\item State the distribution of $X$.
\item Find $\mathrm { P } ( X < 4 )$.
\item Find each of the following.
\begin{itemize}
\item $\mathrm { E } ( X )$
\item $\operatorname { Var } ( X )$
\item The random variable $Y$ is defined by $Y = 10 X + 5$. Find each of the following.
\item $\mathrm { E } ( Y )$
\item $\operatorname { Var } ( Y )$
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2020 Q4 [8]}}