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Poisson distribution and random processes

  1. Nov 11, 2011 #1
    Hello!

    I am writing because I recently became interested in probability distributions, and I have to you a few questions.

    Poisson distribution is given as a probability:

    [itex]f(k;\lambda)=\frac{\lambda^{k}e^{-\lambda}}{k!}[/itex]

    But what is lambda?

    Suppose that we consider as an unrelated incident falling raindrops. If these drops fall 100 in 1 on a surface second how much [itex]\lambda[/itex] will be?

    How to check if the falling drops of rain or some other unrelated events are described in this distribution?
     
    Last edited: Nov 11, 2011
  2. jcsd
  3. Nov 12, 2011 #2
    From Wikipedia: λ is a positive real number, equal to the expected number of occurrences during the given interval. For instance, if the events occur on average 4 times per minute, and one is interested in the probability of an event occurring k times in a 10 minute interval, one would use a Poisson distribution as the model with λ = 10×4 = 40.

    I'm not sure what you mean by "100 in 1."
     
  4. Nov 12, 2011 #3
    Meant falling about 100 drops per second on the area.

    Im curious how can be checked whether a process is described in this distribution.

    For example, the number of drops falling on the glass. How can I check if they are described Poisson distribution.
     
  5. Nov 12, 2011 #4
    I think you would also need a time, since λ measures the expected number of occurrences and not the rate.

    I've only taken one statistics course, but generally the problem will explicitly tell you if it follows a Poisson distribution. There are tests for Poission distributions if you're doing "real world" statistics, but I don't know anything about such tests. Maybe try googling "Poisson distribution test."
     
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