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How is the Poisson Distribution derived? watch

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    (Original post by imsoanonymous123)
    ok thanks for your time anyway =)
    my pleasure (bro)
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    (Original post by TeeEm)
    my pleasure (bro)
    *cringes*
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    (Original post by Gome44)
    *cringes*
    I was called a bro ...
    so it is good etiquette to reply appropriately.
    (I am slowly becoming a mathematician from da hood)
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    (Original post by TeeEm)
    fact one
    all the terms of this infinite series add up to 1
    Thus it may represent a discrete probability distribution

    fact two
    for any discrete random variable E(X) = SUM(xP(X=x)
    For this probability distribution we get EXPECTATION = λ

    fact three
    for any discrete random variable Var(X) = E(X2)- [E(X)]2, where E(X2) = SUM(x2P(X=x)
    For this probability distribution we get VARIANCE = λ

    conclusion
    this infinite series may define a discrete probability distribution with mean and variance λ.

    END OF TRANSMISSION
    What I'm asking is:
    I'm assuming somebody required the use of a probability distribution where the expected value was equal to the variance; for whatever reason. They needed to formulate such an expression first! They couldn't just have known e had something to do with it?!

    I'm guessing the first step looked smoothing like this; but I have no nowhere near the grasp of this to understand where to go next.

    Var(X) = \dfrac{\displaystlye\sum x_i^2}{n} - \mu ^2 = E(X) = \mu
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    (Original post by Callum Scott)
    What I'm asking is:
    I'm assuming somebody required the use of a probability distribution where the expected value was equal to the variance; for whatever reason. They needed to formulate such an expression first! They couldn't just have known e had something to do with it?!

    I'm guessing the first step looked smoothing like this; but I have no nowhere near the grasp of this to understand where to go next.

    Var(X) = \dfrac{\displaystlye\sum x_i^2}{n} - \mu ^2 = E(X) = \mu
    what you are asking is valid but I do not know if that has any statistical importance in order to start the searching from there.

    I stand corrected (if I am wrong) but I think you would start from a theoretical probability distribution and then you determine the mean and variance.

    then it can be used and goodness of fit test can be used.
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    (Original post by TeeEm)
    I was called a bro ...
    so it is good etiquette to reply appropriately.
    (I am slowly becoming a mathematician from da hood)
    Did you watch straight outta Compton or something?
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    (Original post by Callum Scott)
    What I'm asking is:

    stuff

    ]
    I'm just about to go out, but I think you've been given a bit of a runaround in this thread!

    The Poisson distribution is actually derived as a limiting case of the binomial distribution. You should be able to find a derivation in a 'decent' stats book, but if you Google "poisson distribution limiting case of binomial" you should find some helpful links to articles, some of which should be written in a language that's accessible to a competent A level student i.e. doesn't require any additional knowledge
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    (Original post by Gome44)
    Did you watch straight outta Compton or something?
    spending enough time here is adequate for my urban language enrichment.
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    Poisson is piss. **** the proof though.
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    (Original post by Mehrdad jafari)
    Will you recall the concept in 2 years time if you don't learn the proof?
    I won't need to know it in 2 years time or I can relearn it lal


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    (Original post by Callum Scott)
    What I'm asking is:
    I'm assuming somebody required the use of a probability distribution where the expected value was equal to the variance; for whatever reason. They needed to formulate such an expression first! They couldn't just have known e had something to do with it?!

    I'm guessing the first step looked smoothing like this; but I have no nowhere near the grasp of this to understand where to go next.

    Var(X) = \dfrac{\displaystlye\sum x_i^2}{n} - \mu ^2 = E(X) = \mu
    I really like your way of thinking.
    Perhaps if you say Var(X)=E(X) you may find other distributions(not only the Poisson). I know how you feel about this topic; as if you are trying to solve a quadratic equation and everyone says one root verifies the equation -end of the story- but there is another one as well...
    Two scenarios :
    1) Poisson dist. is the ONLY ''root''
    2) Var(x)=E(x) randomly occurs for this dist. -it is not the definition. An event is happening λ times per unit time: if we divide unit time in n intervals the p of happening in each interval is λ/n. That would be a binomial dist. if time wasn't continious so that n tends to infinity...this is a much more important reason to create a dist. than the former case.
    Finally, I don't know the answer as well as for normal dist.
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    (Original post by TeeEm)
    spendin' da time here is sick for my swag language enrichment bro.
    ftfy
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    (Original post by imsoanonymous123)
    ftfy

    seen.
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    (Original post by Kenan and Kel)
    Poisson is piss. **** the proof though.
    Why to do so?Perhaps mathematical curiosity is not one of your traits. Maybe faith is the one for you
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    shhh it's a level maths. don't ask questions about anything that isn't in the spec
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    (Original post by Vesniep)
    Why to do so?Perhaps mathematical curiosity is not one of your traits. Maybe faith is the one for you
    Ain't nobody got time for proofs. Didn't you learn anything from Professor Umbridge? School is all about smashing exams.
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    (Original post by TeeEm)
    I would sincerely love to help you further, but at the moment I am working myself and we are going around in circles as I am a terrible teacher.

    Hopefully someone else will come along and might find the "right" words to explain it better.
    this blog should prove of interest to Poisson fans:

    https://probabilityandstats.wordpres...-distribution/
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    (Original post by the bear)
    this blog should prove of interest to Poisson fans:

    https://probabilityandstats.wordpres...-distribution/
    Definitely NOT a fan of any stats ...
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    (Original post by Kenan and Kel)
    Ain't nobody got time for proofs. Didn't you learn anything from Professor Umbridge? School is all about smashing exams.
    Wait is Umbridge from Harry Potter? It's been a long time since watching these movies and don't remember her attitude towards education.
    Why are you mean with proofs? They are really important for mathematics . I don't say that this particular proof will help you with your Alevel exams,but if you want to be a mathematician you'd better be more curious ; discouraging him from finding a proof doesn't make sense to me.
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    (Original post by mrno1324)
    shhh it's a level maths. don't ask questions about anything that isn't in the spec
    Or any other subject for that matter. Fooks me right off. How are you supposed to learn anything if you don't bloody understand it!?
 
 
 
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