| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Arithmetic sequence uniform distribution |
| Difficulty | Standard +0.8 This question requires understanding of discrete uniform distributions over arithmetic sequences, deriving variance using summation formulas (not just recall of standard uniform variance), and then applying probability calculations. The arithmetic sequence setup and algebraic manipulation needed elevate this above routine statistics questions, though it remains accessible with solid A-level technique. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02e Discrete uniform distribution5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | X = 3W – 2 where W has a uniform distribution over |
| Answer | Marks |
|---|---|
| 4 | B1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks | Guidance |
|---|---|---|
| 1.1 | Var(X) = 9× 1 (𝑛2 −1) | |
| 12 | Mark final answer | |
| 6 | (b) | 3 (1002−1)(= |
| Answer | Marks |
|---|---|
| 100 | B1FT |
| Answer | Marks |
|---|---|
| A1 | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | For both |
| Answer | Marks |
|---|---|
| throughout | FT on their Var(X) |
| Answer | Marks |
|---|---|
| For general method stating use W in place of X | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| B1 | For both | |
| ⇒ 21.6… ≤ 𝑤 ≤ 79.3… | M1 | |
| ⇒ 21.6… ≤ 𝑤 ≤ 79.3… | M1 | Convert to bounds for w (accept as |
| Answer | Marks | Guidance |
|---|---|---|
| 100 | A1 | From correct working and values |
Question 6:
6 | (a) | X = 3W – 2 where W has a uniform distribution over
the values {1, 2, …, n} soi
Var(X) = 32 × Var(W)
Var(X) = 3 (𝑛2 −1) oe
4 | B1
M1
A1
[3] | 3.1a
1.2
1.1 | Var(X) = 9× 1 (𝑛2 −1)
12 | Mark final answer
6 | (b) | 3 (1002−1)(=
E(X) = 149.5 SD(X) = √ 86.5…)
4
So require 62.9… ≤ 𝑥 ≤ 236.0…
⇒ 21.6… ≤ 𝑤 ≤ 79.3…
58
Probability = oe
100 | B1FT
B1FT
M1
A1 | 3.1a
1.1
3.1a
1.1 | For both
Evaluate bounds for x (accept as
integers)
Convert to bounds for w (accept as
integers)
From correct working and values
throughout | FT on their Var(X)
FT on their Var(X)
and their E(X)
Alternative for candidates who realise that this can
be done with a uniform distribution on {1, 2, …, n}
For general method stating use W in place of X | B1
1 (1002−1)(=
E(W) = 50.5 SD(W) = √ 28.8…)
12
B1 | For both
⇒ 21.6… ≤ 𝑤 ≤ 79.3… | M1
⇒ 21.6… ≤ 𝑤 ≤ 79.3… | M1 | Convert to bounds for w (accept as
integers)
58
Probability = oe
100 | A1 | From correct working and values
throughout
[4]
PMT
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Please get in touch if you want to discuss the accessibility of resources we offer to support you in delivering our qualifications.6 The random variable $X$ has a uniform distribution over the values $\{ 1,4,7 , \ldots , 3 n - 2 \}$, where $n$ is a positive integer.
\begin{enumerate}[label=(\alph*)]
\item Determine $\operatorname { Var } ( X )$ in terms of $n$.
\item Given that $n = 100$, find the probability that $X$ is within one standard deviation of the mean.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2022 Q6 [7]}}