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What is the name and application of this probability distribution

  1. Mar 1, 2012 #1

    In my homework I've encountered a discrete probability distribution of this form:

    [tex]f(k,\lambda)=N \frac{\lambda^k}{k!}[/tex]

    [tex]k[/tex] is the variable, and [tex]\lambda[/tex] is a parameter. I'm curious what is this distribution - what's its name and where can it be applied. I will be grateful for, for example, redirecting me to the proper wikipedia article. Thanks!
  2. jcsd
  3. Mar 1, 2012 #2
  4. Mar 1, 2012 #3
    Are you sure you copied the formula correctly? The Poisson distribution is defined by:

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

    where [itex] \lambda [/itex] is the rate parameter (expected number of events per unit time), and k is the number of events observed.

    In evaluating Poisson noise the question becomes [itex]P(k=N_t)[/itex] but your formula still doesn't look right since it lacks the exponential term.
    Last edited by a moderator: Mar 2, 2012
  5. Mar 2, 2012 #4
    I think the number N here is used as a normlization factor.

  6. Mar 2, 2012 #5


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    [EDIT]: After reading the wiki page, yes the value depends on lambda not k.

    Can't believe I've used this pdf so many times and forgotten it!
    Last edited: Mar 2, 2012
  7. Mar 2, 2012 #6
    Thank you all for responding. Yes, the number N stand for the normalization constant, and in the wikipedia article posted by micromass the exponent is exactly the normalization:

    so i does not vary with k.
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