OCR MEI Further Statistics A AS Specimen — Question 2 6 marks

Exam BoardOCR MEI
ModuleFurther Statistics A AS (Further Statistics A AS)
SessionSpecimen
Marks6
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Mark schemeDownload PDF ↗
TopicChi-squared goodness of fit
TypeChi-squared goodness of fit: Uniform
DifficultyModerate -0.8 This is a straightforward uniform distribution question requiring only basic probability calculations. Part (i) is direct counting, part (ii) applies independence with simple multiplication, and part (iii) requires finding the mean then counting. No chi-squared testing is actually involved despite the topic label, and all parts are routine applications of definitions with no problem-solving insight needed.
Spec5.02e Discrete uniform distribution
2 The discrete random variable \(Y\) is uniformly distributed over the values \(\{ 12,13 , \ldots , 20 \}\).
  1. Write down \(\mathrm { P } ( Y < 15 )\).
  2. Two independent observations of \(Y\) are taken. Find the probability that one of these values is less than 15 and the other is greater than 15 .
  3. Find \(\mathrm { P } ( Y > \mathrm { E } ( Y ) )\).
Question 2:
AnswerMarks Guidance
2(i) 1 1 1 1
P (Y < 15) = (cid:14) (cid:14) (cid:32)
AnswerMarks
9 9 9 3B1
[1]I
1.1M
(ii)E
1 5 5 1
(cid:117) (cid:14) (cid:117)
3 9 9 3
P
10
=
AnswerMarks
27C
B1
M1
A1
AnswerMarks
[3]1.1
3.1a
AnswerMarks
1.15
For
9
For sum of two products of
fractions
FT from (i) if all probabilities in
(0, 1)
AnswerMarks
(iii)S
E(Y) =16
4
P(Y>16)=
AnswerMarks
9B1
B1
AnswerMarks
[2]1.1
1.1soi
FT their E(Y) if in [15,17]
AnswerMarks Guidance
22 2
AnswerMarks Guidance
2(i)1 0
AnswerMarks Guidance
2(ii)2 0
3
AnswerMarks Guidance
2(iii)2 0 
Question 2:
2 | (i) | 1 1 1 1
P (Y < 15) = (cid:14) (cid:14) (cid:32)
9 9 9 3 | B1
[1] | I
1.1 | M
(ii) | E
1 5 5 1
(cid:117) (cid:14) (cid:117)
3 9 9 3
P
10
=
27 | C
B1
M1
A1
[3] | 1.1
3.1a
1.1 | 5
For
9
For sum of two products of
fractions
FT from (i) if all probabilities in
(0, 1)
(iii) | S
E(Y) =16
4
P(Y>16)=
9 | B1
B1
[2] | 1.1
1.1 | soi
FT their E(Y) if in [15,17]
2 | 2 | 2 | 3 | 4 | 5 | 6
--- 2(i) ---
2(i) | 1 | 0 | 0 | 0 | 1
--- 2(ii) ---
2(ii) | 2 | 0 | 1 | 0 | N
3
--- 2(iii) ---
2(iii) | 2 | 0 | 0 | 0 | 2
2 The discrete random variable $Y$ is uniformly distributed over the values $\{ 12,13 , \ldots , 20 \}$.\\
(i) Write down $\mathrm { P } ( Y < 15 )$.\\
(ii) Two independent observations of $Y$ are taken. Find the probability that one of these values is less than 15 and the other is greater than 15 .\\
(iii) Find $\mathrm { P } ( Y > \mathrm { E } ( Y ) )$.

\hfill \mbox{\textit{OCR MEI Further Statistics A AS  Q2 [6]}}
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Q1 6 Q2 6 Q3 10 Q4 18 Q5 8 Q6 12