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Date May 2017 Marks available 4 Reference code 17M.1.hl.TZ2.7
Level HL only Paper 1 Time zone TZ2
Command term Find Question number 7 Adapted from N/A

Question

The random variable XX has the Poisson distribution Po(m)Po(m). Given that P(X>0)=34P(X>0)=34, find the value of mm in the form lnalna where aa is an integer.

[3]
a.

The random variable YY has the Poisson distribution Po(2m)Po(2m). Find P(Y>1)P(Y>1) in the form blnccblncc where bb and cc are integers.

[4]
b.

Markscheme

P(X>0)=1P(X=0)P(X>0)=1P(X=0)     (M1)

1em=341em=34 or equivalent     A1

m=ln4m=ln4     A1

[3 marks]

a.

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

=1e2ln4e2ln4×2ln4=1e2ln4e2ln4×2ln4     A1

recognition that 2ln4=ln162ln4=ln16     (A1)

P(Y>1)=15ln1616P(Y>1)=15ln1616     A1

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 5 - Core: Statistics and probability » 5.6
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