| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Standard +0.3 This is a straightforward application of discrete uniform distribution properties. Part (a) requires counting integers and forming a probability fraction, while part (b) uses the standard variance formula Var(ΣXᵢ) = ΣVar(Xᵢ) with the known variance formula for discrete uniform distributions. Both parts are routine calculations with no novel insight required, making it slightly easier than average. |
| Spec | 5.02c Linear coding: effects on mean and variance5.02e Discrete uniform distribution |
| Answer | Marks | Guidance |
|---|---|---|
| 9 | (a) | 1(n+1) |
| Answer | Marks |
|---|---|
| 2(2n+1) | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | For correct denominator |
| Answer | Marks | Guidance |
|---|---|---|
| 9 | (b) | (2n + 1) values so Var(X)= 1 [ (2n+1)2−1] |
| Answer | Marks |
|---|---|
| 3 3 | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | Allow M1 for 10 any |
Question 9:
9 | (a) | 1(n+1)
P(X > 1n)= 2
2 2n+1
n+1
=
2(2n+1) | M1
M1
A1
[3] | 3.1a
1.1
1.1 | For correct denominator
For correct numerator
9 | (b) | (2n + 1) values so Var(X)= 1 [ (2n+1)2−1]
12
Var of sum of 10 values =10× 1 [(2n+1)2−1]
12
=10n2+10n
3 3 | M1
M1
A1
[3] | 3.1a
1.1
1.1 | Allow M1 for 10 any
attempt at variance
×9 The discrete random variable $X$ has a uniform distribution over the set of all integers between $- n$ and $n$ inclusive, where $n$ is a positive integer.
\begin{enumerate}[label=(\alph*)]
\item Given that $n$ is odd, determine $\mathrm { P } \left( \mathrm { X } > \frac { 1 } { 2 } \mathrm { n } \right)$, giving your answer as a single fraction in terms of $n$.
\item Determine the variance of the sum of 10 independent values of $X$, giving your answer in the form $\mathrm { an } ^ { 2 } + \mathrm { bn }$, where $a$ and $b$ are constants.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2021 Q9 [6]}}