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I was wondering what kind of distribution applies to a variable that can have one of two outcomes (say yes or no) but the probability of any of these outcomes is completely random and cannot he determined ?

Example: I am stopping 10,000 people on the street and asking them: are you happy today.

Thank you !

Jay Kay
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  • Well, isn't this simply a bernoulli process with an unknown success probability? Same as if I handed you a coin, told you that it wasn't necessarily fair, but declined to tell you what the probability of getting Heads was. – lulu Jan 01 '19 at 14:18
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    And the conjugate prior family for a Bernoulli or binomial random variable are Beta distributions – Henry Jan 01 '19 at 16:15
  • Thank you very much. This is extremely useful. Thing is I’m struggling to set up confidence intervals with such an experiment. When using standard distributions it’s very straightforward for me. It would be amazing if you could shed some light on that i.e. testing for statistical significance using a Bernoulli random variable. I’ve actually taken the time to collect this data first hand and am playing around with it. Thank you ! – Jay Kay Jan 01 '19 at 20:06
  • Also correct me if I’m wrong but a Bernoulli distribution has the same probability p for each outcome (consistent unfairness) but in the case of asking people whether they are happy or not, the probability of their answer (yes/no) is changing all the time since it is a subjective question. – Jay Kay Jan 01 '19 at 20:21
  • ... it could be a Poisson Binomial Distribution. – Jay Kay Jan 01 '19 at 20:33

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