Transcript Poisson Statistics MCH Sem3

Poisson Statistics
Poisson Distribution and Standard Deviation
By Rachel Furhang
Poisson Distribution
notation:
μ- the mean number of succeses that
occur in a specified region
x- the actual number of succeses that
occur in a specified region
e- constant equaling about 2.71828
P(x,μ): The Poisson probability that exctly
x successes occur in a Poisson experiment
when the mean number of successes is μ.
Formula: P(x,
x
μ)=e μ(μ )/x
Example:
If the average amount of papers you have
to write per week is 4, what is the
probability that you will only need to
write 1 paper next week (your birthday)?
P(1,4)=e-4(41)/1
The probability is .073
Standard Deviation(σ)
2
(σ ):
Variance
When you want to know how
accurate your mean is.
How: Find the difference of each data point
from the mean value, square all those values,
and find the mean of those values.
Standard Deviation is the square root of
the variance.
Example:
Finding the standard deviation of the test grades of
your classmates.
Data:
82,85,92,95,88,97,95,85,0,87,95,0
Add these up and divide by 12, to get a mean score of
75.
Then find the variance, which is 1148.75
The standard deviation is the square root of that,
33.89
So all values not within 33.89 of the mean are
outside of the standard deviation.
The Poisson distribution graph shows the likelihood
that an event that occurs at rate λ will occur a
specific amount of times.
www.uh.edu
Umass.edu
References: Khan academy statistics videos, MIT department of physics lessons,
University of Massachusetts online lessons.