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Math Help - Difference between binomial distribution and geometric, hypergeometric etc

  1. #1
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    Difference between binomial distribution and geometric, hypergeometric etc

    Hello,

    I'm confused about the difference between binomial, geometric, hypergeometric, negative binomial, and discrete distribution. When I get a word problem, I always use the incorrect one.

    For binomial: it's just the x successes in n trails where the probability of success in each trail is the same right?

    but isn't this the same as geometric?

    i know that hypergeometic is basically like the binomial except it's without replacement (the prob changes within each trail)

    and that the negative deals with drawing the nth time right?

    Thank you!
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  2. #2
    MHF Contributor matheagle's Avatar
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    binomial, geo and neg binomial should be considered together.
    ALL of these are discrete by the way.
    In those three, we do an experiment repeatedly
    The chance of success is always p and it stays p from trial to trial
    NOT trail.
    IN the bio case, we are doing this experiment n times.
    n is fixed in advance
    The random variable, X is the number of successes out of those n.
    There are two outcomes and a success is one of the two you decide on in advance.

    Then with the geo and the neg binomial, you still do this success/failure experiment repeatedly
    HERE Y is a geometric, IT is the trial on which we observe the FIRST success.
    Now some people say that's including that trial. some count all the previous trial and not that last one.
    For example if we are waiting for a HEAD, when tossing a coin and we see TTH, then Y=3 or 2 depending on how you define that geo.

    The neg bio is the same as a geo, but here you are waiing for the second or third.... success.
    It can be viewed as the sum of r independent geometrics.
    That is the easiest way to obtain its mean and variance
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  3. #3
    MHF Contributor matheagle's Avatar
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    all of these are discrete (binomial, geometric, hypergeometric, negative binomial) Poisson...
    the others are continuous (gamma, exponential, normal, t, f, uniform, beta ....)
    you can have mixtures of these, but that's unusual

    For a distribution to be discrete, there is a countable (small) set of outcomes, that includes the natural numbers 1,2,3...
    In the continuous setting there are way too many realizations (outcomes) like all the real number is in (0,1)
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