In a poisson distribution , probability for x= 0 is 10% What is the mean of the distribution
Answers
The Poisson random variable satisfies the following conditions:
The number of successes in two disjoint time intervals is independent.
The probability of a success during a small time interval is proportional to the entire length of the time interval.
Apart from disjoint time intervals, the Poisson random variable also applies to disjoint regions of space.
Answer:
The Poisson random variable satisfies the following conditions:
The number of successes in two disjoint time intervals is independent.
The probability of a success during a small time interval is proportional to the entire length of the time interval.
Apart from disjoint time intervals, the Poisson random variable also applies to disjoint regions of space.
Applications
the number of deaths by horse kicking in the Prussian army (first application)
birth defects and genetic mutations
rare diseases (like Leukemia, but not AIDS because it is infectious and so not independent) - especially in legal cases
car accidents
traffic flow and ideal gap distance
number of typing errors on a page
hairs found in McDonald's hamburgers
spread of an endangered animal in Africa
failure of a machine in one month
Notation
We use upper case variables (like X and Z) to denote random variables, and lower-case letters (like x and z) to denote specific values of those variables.
The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:
\displaystyle{P}{\left({X}\right)}=\frac{{{e}^{-\mu}\mu^{x}}}{{{x}!}}P(X)=
x!
e
−μ
μ
x
where
\displaystyle{x}={0},{1},{2},{3}\ldotsx=0,1,2,3…
\displaystyle{e}={2.71828}e=2.71828 (but use your calculator's e button)
\displaystyle\mu=μ= mean number of successes in the given time interval or region of space
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