The document discusses the Poisson distribution, which models the probability of a number of random events occurring in a fixed interval of time or space. The Poisson distribution was developed by Simeon Poisson in 1837 to analyze counts of events like disease cases, accidents, or births that happen randomly. It is used when the mean number of occurrences in each interval is known but the number in any given interval varies randomly. Examples where it applies include machine failures, traffic flow, typing errors, and animal populations.

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 The Poisson Distribution was developed by
the French mathematician Simeon Denis
Poisson in 1837.

3.  The Poisson distribution is a discrete
probability distribution for the counts of
events that occur randomly in a given interval
of time (or space).
 Many experimental situations occur in which
we observe the counts of events within a set
unit of time, area, volume, length etc.
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4. The probability of observing x events in a given
interval is given by,
e is a mathematical constant. e≈2.718282
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5. 1:The number of cases of a disease in different
towns.
2: Number of industrial accidents per month in
a manufacturing plant.
3: Births in a hospital occur randomly at an
average every day.
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6.  Poisson process is a random process which
counts the number of events and the time
that these events occur in a given time
interval. The time between each pair of
consecutive events has an exponential
distribution with parameter λ and each of
these inter-arrival times is assumed to be
independent of other inter-arrival times.
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7.  Poisson distributions are useful to model
events that seem to take place over and over
again in a completely haphazard way.
 If a mean or average probability of an event
happening per unit time/per page/per mile
cycled etc., is given, and you are asked to
calculate a probability of n events happening
in a given time/number of pages/number of
miles cycled, then the Poisson Distribution is
used
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8. binomial poisson
 Fixed Number of Trials
(n) [10 pie throw
 Only 2 Possible
Outcomes [hit or miss]
]
 Infinite Number of Trial
 Unlimited Number of
Outcomes Possible
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10. Let’s continue to assume we have a continuous
variable x and graph the Poisson Distribution, it will
be a continuous curve, as follows:
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11. ◦ A practical application
of this distribution was made
by Ladislaus Bortkiewicz in 1898
when he was given the task of
investigating the number of
soldiers in the Russian army
killed accidentally by horse
kicks this experiment
introduced the Poisson distribution
to the field of reliability engineering.
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12. i. The number of deaths by horse kicking in
the Russian army •
ii. Birth defects and genetic mutations •
iii. Rare diseases.
iv. Traffic flow and ideal gap distance •
v. Number of typing errors on a page •
vi. Spread of an endangered animal in Africa •
vii. Failure of a machine in one month.
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