| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2019 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Variance of sum of independent values |
| Difficulty | Standard +0.3 This is a straightforward application of discrete uniform distribution properties. Part (a) is immediate recognition, (b) is simple counting, (c)(i) uses the standard result that Var(X+Y+Z)=Var(X)+Var(Y)+Var(Z) for independent variables, and (c)(ii) requires multinomial probability calculation with clearly defined events. All techniques are standard for this specification with no novel insight required, making it slightly easier than average. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.02e Discrete uniform distribution |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (a) | Uniform |
| on the values {10, 20, ..., 80} | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.2 | For uniform |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | P(X 40)5 | |
| 8 | B1 | |
| [1] | 1.1 | |
| (c) | (i) | 82 1 |
| Answer | Marks |
|---|---|
| So variance for 3 rolls = 1575 | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.3 |
| Answer | Marks |
|---|---|
| 1.1 | Or M1 for applying E[X2] – E2[X] to correct distribution |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | (ii) | P(X 30) 1, P(30 X 50)P(X 50) 3 |
| Answer | Marks |
|---|---|
| 128 | B1 |
| Answer | Marks |
|---|---|
| [3] | 3.1a |
| Answer | Marks |
|---|---|
| 1.1 | For any one of these |
Question 3:
3 | (a) | Uniform
on the values {10, 20, ..., 80} | B1
B1
[2] | 3.3
1.2 | For uniform
For values of uniform distribution stated
SC1 For case when ‘uniform’ not stated but correct
uniform distribution is tabulated.
(b) | P(X 40)5
8 | B1
[1] | 1.1
(c) | (i) | 82 1
102
Variance for 1 roll =
12
= 525
So variance for 3 rolls = 1575 | M1
A1
B1
[3] | 3.3
1.1
1.1 | Or M1 for applying E[X2] – E2[X] to correct distribution
FT for 3×their variance for 1 roll
(c) | (ii) | P(X 30) 1, P(30 X 50)P(X 50) 3
4 8
Required probability = 6133
4 8 8
= 27 or 0.2109
128 | B1
M1
A1
[3] | 3.1a
1.1
1.1 | For any one of these
For 6×product of their three probabilities
Allow 0.211www or 0.21www3 A fair 8 -sided dice has faces labelled 10, 20, 30, ..., 80 .
\begin{enumerate}[label=(\alph*)]
\item State the distribution of the score when the dice is rolled once.
\item Write down the probability that, when the dice is rolled once, the score is at least 40 .
\item The dice is rolled three times.
\begin{enumerate}[label=(\roman*)]
\item Find the variance of the total score obtained.
\item Find the probability that on one of the rolls the score is less than 30 , on another it is between 30 and 50 inclusive and on the other it is greater than 50 .
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2019 Q3 [9]}}