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. KARACHI GRAMMAR SCHOOL

A Level Mathematics – S2

POISSON DISTRIBUTION

CAIE Syllabus

Notes compiled by

Tahmeena Khan

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Real Life Application of Poisson distribution:

Whether one observes patients arriving at an emergency room, cars driving up to a gas

station, decaying radioactive atoms, bank customers coming to their bank, or shoppers

being served at a cash register, the streams of such events typically follow the Poisson

process. The underlying assumption is that the events are statistically independent and the

rate, µ, of these events (the expected number of the events per time unit) is constant. The

list of applications of the Poisson distribution is very long. To name just a few more:

• The number of bankruptcies that are filed in a month (Jaggia, Kelly, 2012 p.158).

• The number of arrivals at a car wash in one hour (Anderson et al., 2012, p. 236).

• The number of network failures per day (Levine, 2010, p. 197).

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Past Paper Questions:

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(Nov. 09/71/2 ans i- 0.987 ii- 0.902)

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(Nov. 09/71/3 ans. i – 0.202, ii – 0.159)

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(June 15/72/3 ans. 150, 30000)

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(June 17/73/5; ans. i –a) 0.65; b- >15 ii – a)0.121; b) np<5)

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5.

( Nov.13/72/4 ; i – 0.469 ; ii- 2.15 min.)

6.

Ans.i) 0.122 ii) 0.532 iii) 0.0135 iv) 0.229

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Answer

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