poisson or binomial distribution

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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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.

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A typist makes on average 2 mistakes per page. What is theprobability of a particular page having no errors on it?

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X

Po(=2) where Xcounts the number of mistakes per page.

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X

Po(

=2) where Xcounts the number of mistakes per page.

Pr(X =0) =20 e2

0! =0.135.

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A computer crashes once every 2 days on average. What is theprobability of there being 2 crashes in one week?

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Again, average rate given: =0.5 crashes/day. Hence, Poisson.

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= (0.5 per day 7 days) =3.5/week. So X Po(=3.5) whereXcounts the number of crashes in one week.

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= (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.



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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)

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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.



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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?

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Binomial distribution. X

b(10,

0.

02)

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Binomial distribution. X

b(10,

0.

02)

Pr(X =2) =

10

2

0.022 0.988 =0.015.

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The mean number of faults in a new house is 8. What is theprobability of buying a new house with exactly 1 fault?


P i Bi i l di ib i ?
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Poisson, X Po(=8), where Xcounts the number of faults in a

new house.


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Poisson, X Po(=8), where Xcounts the number of faults in a

new house.

Pr(X =1) = 81 e8

1! =0.0027.


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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?


P i Bi i l di t ib ti ?
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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).


P i Bi i l di t ib ti ?
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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

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poisson or binomial distribution

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