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Date May Example question Marks available 3 Reference code EXM.1.AHL.TZ0.17
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number 17 Adapted from N/A

Question

Sue sometimes goes out for lunch. If she goes out for lunch on a particular day then the probability that she will go out for lunch on the following day is 0.4. If she does not go out for lunch on a particular day then the probability she will go out for lunch on the following day is 0.3.

Write down the transition matrix for this Markov chain.

[2]
a.

We know that she went out for lunch on a particular Sunday, find the probability that she went out for lunch on the following Tuesday.

[2]
b.

Find the steady state probability vector for this Markov chain.

[3]
c.

Markscheme

(0.40.30.60.7)(0.40.30.60.7)      M1A1

[2 marks]

a.

(0.40.30.60.7)2(10)=(0.340.66)(0.40.30.60.7)2(10)=(0.340.66)     M1

So probability is 0.34       A1

[2 marks]

b.

(0.40.30.60.7)(p1p)=(p1p)0.4p+0.3(1p)=pp=13(0.40.30.60.7)(p1p)=(p1p)0.4p+0.3(1p)=pp=13    M1A1

So vector is (1323)(1323)       A1

[or by investigating high powers of the transition matrix]

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » AHL 4.19—Transition matrices – Markov chains
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Topic 4—Statistics and probability

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