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8/13/2019 Poisson or Binomial Distribution
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Poisson or Binomial distribution?
() Poisson or Binomial distribution? 1 / 8
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Poisson or Binomial distribution?
If a mean or average probability of an event happening per unittime/per page/per mile cycled etc., is given, and you are asked tocalculate a probability of n events happening in a given time/number
of pages/number of miles cycled, then the Poisson Distribution isused.
If, on the other hand, an exact probability of an event happening isgiven, or implied, in the question, and you are asked to caclulate theprobability of this event happening k times out of n, then the
Binomial Distribution must be used.
() Poisson or Binomial distribution? 2 / 8
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Poisson or Binomial distribution?
A typist makes on average 2 mistakes per page. What is theprobability of a particular page having no errors on it?
() Poisson or Binomial distribution? 3 / 8
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Poisson or Binomial distribution?
A typist makes on average 2 mistakes per page. What is theprobability of a particular page having no errors on it?
X
Po(=2) where Xcounts the number of mistakes per page.
() Poisson or Binomial distribution? 3 / 8
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Poisson or Binomial distribution?
A typist makes on average 2 mistakes per page. What is theprobability of a particular page having no errors on it?
X
Po(
=2) where Xcounts the number of mistakes per page.
Pr(X =0) =20 e2
0! =0.135.
() Poisson or Binomial distribution? 3 / 8
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Poisson or Binomial distribution?
A computer crashes once every 2 days on average. What is theprobability of there being 2 crashes in one week?
() Poisson or Binomial distribution? 4 / 8
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7/21
Poisson or Binomial distribution?
A computer crashes once every 2 days on average. What is theprobability of there being 2 crashes in one week?
Again, average rate given: =0.5 crashes/day. Hence, Poisson.
() Poisson or Binomial distribution? 4 / 8
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8/21
Poisson or Binomial distribution?
A computer crashes once every 2 days on average. What is theprobability of there being 2 crashes in one week?
Again, average rate given: =0.5 crashes/day. Hence, Poisson.
= (0.5 per day 7 days) =3.5/week. So X Po(=3.5) whereXcounts the number of crashes in one week.
() Poisson or Binomial distribution? 4 / 8
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Poisson or Binomial distribution?
A computer crashes once every 2 days on average. What is theprobability of there being 2 crashes in one week?
Again, average rate given: =0.5 crashes/day. Hence, Poisson.
= (0.5 per day 7 days) =3.5/week. So X Po(=3.5) whereXcounts the number of crashes in one week.
Pr(X =2) = 3.52 e3.5
2! =0.185.
() Poisson or Binomial distribution? 4 / 8
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8/13/2019 Poisson or Binomial Distribution
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Poisson or Binomial distribution?
Components are packed in boxes of 20. The probability of acomponent being defective is 0.1. What is the probability of a boxcontaining 2 defective components?
Binomial, with n=20. X b(20, 0.1)
() Poisson or Binomial distribution? 5 / 8
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Poisson or Binomial distribution?
Components are packed in boxes of 20. The probability of acomponent being defective is 0.1. What is the probability of a boxcontaining 2 defective components?
Binomial, with n=20. X b(20, 0.1)
So
Pr(X=2) =
20
2
0.12 0.918 =0.285.
() Poisson or Binomial distribution? 5 / 8
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Poisson or Binomial distribution?
ICs are packaged in boxes of 10. The probability of an ic being faultyis 2%. What is the probability of a box containing 2 faulty ics?
() Poisson or Binomial distribution? 6 / 8
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Poisson or Binomial distribution?
ICs are packaged in boxes of 10. The probability of an ic being faultyis 2%. What is the probability of a box containing 2 faulty ics?
Binomial distribution. X
b(10,
0.
02)
() Poisson or Binomial distribution? 6 / 8
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Poisson or Binomial distribution?
ICs are packaged in boxes of 10. The probability of an ic being faultyis 2%. What is the probability of a box containing 2 faulty ics?
Binomial distribution. X
b(10,
0.
02)
Pr(X =2) =
10
2
0.022 0.988 =0.015.
() Poisson or Binomial distribution? 6 / 8
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Poisson or Binomial distribution?
The mean number of faults in a new house is 8. What is theprobability of buying a new house with exactly 1 fault?
() Poisson or Binomial distribution? 7 / 8
P i Bi i l di ib i ?
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Poisson or Binomial distribution?
The mean number of faults in a new house is 8. What is theprobability of buying a new house with exactly 1 fault?
Poisson, X Po(=8), where Xcounts the number of faults in a
new house.
() Poisson or Binomial distribution? 7 / 8
P i Bi i l di ib i ?
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Poisson or Binomial distribution?
The mean number of faults in a new house is 8. What is theprobability of buying a new house with exactly 1 fault?
Poisson, X Po(=8), where Xcounts the number of faults in a
new house.
Pr(X =1) = 81 e8
1! =0.0027.
() Poisson or Binomial distribution? 7 / 8
P i Bi i l di ib i ?
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Poisson or Binomial distribution?
A box contains a large number of washers; there are twice as manysteel washers as brass ones. Four washers are selected at random
from the box. What is the probability that 0, 1, 2, 3, 4 are brass?
() Poisson or Binomial distribution? 8 / 8
P i Bi i l di t ib ti ?
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Poisson or Binomial distribution?
A box contains a large number of washers; there are twice as manysteel washers as brass ones. Four washers are selected at random
from the box. What is the probability that 0, 1, 2, 3, 4 are brass?Binomial distribution with X b(p=1/3, n=4).
() Poisson or Binomial distribution? 8 / 8
P i Bi i l di t ib ti ?
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Poisson or Binomial distribution?
A box contains a large number of washers; there are twice as manysteel washers as brass ones. Four washers are selected at random
from the box. What is the probability that 0, 1, 2, 3, 4 are brass?Binomial distribution with X b(p=1/3, n=4).
Pr(X = 0) = 4
0
1
3
0
2
3
4
=0.197 53
Pr(X = 1) =
4
1
1
3
1
2
3
3=0.395 06
Pr(X = 2) = 42 1
3
2
23
2
=0.296 30
Pr(X = 3) =
4
3
1
3
3
2
3
1=0.098765
Pr(X = 4) = 44 1
3
4
23
0
=0.01 234 6
() Poisson or Binomial distribution? 8 / 8
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