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 X has the Poisson distribution Po(m). Given that P(X>0)=34, find the value of m in the form lna where a is an integer.
[3]
a.
The random variable Y has the Poisson distribution Po(2m). Find P(Y>1) in the form b−lncc where b and c are integers.
[4]
b.
Markscheme
P(X>0)=1−P(X=0) (M1)
⇒1−e−m=34 or equivalent A1
⇒m=ln4 A1
[3 marks]
a.
P(Y>1)=1−P(Y=0)−P(Y=1) (M1)
=1−e−2ln4−e−2ln4×2ln4 A1
recognition that 2ln4=ln16 (A1)
P(Y>1)=15−ln1616 A1
[4 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
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