Poisson Definition and 509 Threads

In probability theory and statistics, the Poisson distribution (; French pronunciation: [pwasɔ̃]), named after French mathematician Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.
For instance, a call center receives an average of 180 calls per hour, 24 hours a day. The calls are independent; receiving one does not change the probability of when the next one will arrive. The number of calls received during any minute has a Poisson probability distribution: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very small probability it could be 10. Another example is the number of decay events that occur from a radioactive source during a defined observation period.

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  1. S

    Poisson distribution question

    ok, so on average, there is a chromosome mutation link once every 10,000 baby births. approximate the probability that exactly 3 of the next 20,000 babies born will have the mutation. so using poisson distribution, I let p = 1/10,000 n = 20,000. and use formula (e^(-np) * (np)^k /...
  2. S

    About the basics of Poisson bracket

    Dear all, Please help me to solve the following problems about Poisson brackets. Let M be a 2n-manifold and w is a closed non-degenerate di®eren- tial 2-form. (Locally we write w = w_ij dx^i ^ dx^j with [w_ij ] being a non-degenerate anti-symmetric real matrix-valued local function on M)...
  3. B

    Calculating Poisson Distribution for Car Backfire Frequency on City Streets

    Hello In my text the following question is posed: ON a city street, car backfires are heard 8 times per hour. Use the poisson distribution to find an exact expression for the prob. that a car backfire is heard at most once in a given hour. Do not simplify or evaluate your answer. Now...
  4. L

    Non-degenerate Poisson bracket and even-dimensional manifold

    From this reference: titled From Classical to Quantum Mechanics, I quote the following: ( \xi^i are coordinate functions) Let M be a manifold of dimension n. If we consider a non-degenerate Poisson bracket, i.e. such that \{\xi^i,\xi^j\} \equiv \omega^i^j is an inversible...
  5. B

    Poisson summation and Parsevals identity

    I've heard something about Poisson summation in relation to Fourier analysis, but I can't seem to find any good info on the subject... Can anyone explain what "Poisson summation" is? Furthermore, I would like to know exactly what "Parsevals identity" states and how it is applied. Thanks.
  6. denian

    Minimum Occupants for Probability of Fishing > 0.7

    in a town, one of a hundred occupants loves fishing. what is the minimum occupants must be chosen so that the probability that there is at least one occupant who loves fishing is more than 0.7? i hope u understand the question, because I am doing some direct translation from my language to...
  7. F

    Question about poisson distributed variables

    Hi, I'm trying to prove if X~Po(m) => 2X~Po(2m) But I'm not sure how to prove or disprove it. I'm thinking about using the addition formula, but is this the right approach? X_1~Po(m) X_2~Po(n) X_1+X_2~Po(m+n) n=m => X_1=X_2 => 2X_1~Po(2m) Any help is appreciate. Thanks /farbror
  8. S

    Poisson stats: signal to noise

    A star was measured to have an apparent magnitude m=16 with S/N=10 integrated over a minute. What is the uncertainty in the measurement? signal=flux*area*time noise=sqrt(signal)=sqrt(fAt) So, S/N=sqrt(fAt) How can I find fA? m=-2.5logfAt+K 16=-2.5log(fAt)+K Hoping that K is arbitrary...
  9. O

    What is the Probability of Losing in a Lottery with 20,000,000 Tickets?

    If you have a lottery (Megamillions) and you sell 20,000,000 tickets, the probability of them all losing is given by: (135,145,919/135,145,920)^20,000,000 = 0.862448363 A close approximation is given by: e^-(20,000,000/135,145,920) = 0.8624413 I just learned this from a book. That's...
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