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Date May 2017 Marks available 3 Reference code 17M.1.AHL.TZ2.H_7
Level Additional Higher Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number H_7 Adapted from N/A

Question

The random variable X has the Poisson distribution Po ( m ) . Given that P ( X > 0 ) = 3 4 , find the value of m in the form ln a where a is an integer.

[3]
a.

The random variable Y has the Poisson distribution Po ( 2 m ) . Find P ( Y > 1 ) in the form b ln c c where b and c are integers.

[4]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

P( X > 0 ) = 1 P( X = 0 )      (M1)

1 e m = 3 4 or equivalent     A1

m = ln 4      A1

[3 marks]

a.

P ( Y > 1 ) = 1 P ( Y = 0 ) P ( Y = 1 )      (M1)

= 1 e 2 ln 4 e 2 ln 4 × 2 ln 4      A1

recognition that 2 ln 4 = ln 16      (A1)

P ( Y > 1 ) = 15 ln 16 16      A1

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » AHL 4.17—Poisson distribution
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Topic 4—Statistics and probability

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