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    It's just the PMF of the distribution at 0,1,2,3...

    It's just the PMF of the distribution at 0,1,2,3 and 4 for each curve (its maximum for one is bimodal at 499999 and 500000 trials). Hope that clarifies it for you.
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    That would of course be the binomial...

    That would of course be the binomial distribution. Here's the PMF for 0 to 4 seen by trials:

    152689

    Note that these are not a "bellcurve" - the probability is much too low for the # of trials...
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    No, it's not. You are ~1.85 X more likely get...

    No, it's not.

    You are ~1.85 X more likely get you first success on trial 346575 versus trial 653425.

    The distribution of trials to first success is most certainly *not* a "bellcurve", it is a...
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    Bold emphasis mine: Careful with your wording...

    Bold emphasis mine: Careful with your wording there. 500k is *not* the most likely (which is of course 1, the mode of the distribution. IOW, you are *most likely* to succeed on the first attempt...
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    Not at all how I read it, nor based on that...

    Not at all how I read it, nor based on that poster's other replies what they meant.

    It is, in fact, the very definition in probability: *Expectation*, which *is* 1 for the example the poster gave.
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