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Aug 4, 2023 at 10:31 comment added Tim @AntonKerel so you want to know what is the probability of seeing 3 successes in 40 trials given that the probability of success is $\mu$ given the posterior beta distribution? This is what I described.
Aug 4, 2023 at 10:17 comment added Anton Kerel Thank you, Tim. Sorry for a question that is a bit confusing. You almost understood my question. I can rephrase it a bit. I want to produce a (biased) Bayesian esimator of probability of having 3 successes in 40 tosses given the posterior distribution that I have estimated before. In my mind, Bayesian model always produces a probability of some sort. You can then use the pdf of the posterior to do inference. Therefore, I am interested in the probability of success for 40 choose 3 given that my coin priorly has been estimate to follow $Beta(2,99)$. Does this make sense?
Aug 3, 2023 at 15:41 history edited Tim CC BY-SA 4.0
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Aug 3, 2023 at 15:34 history answered Tim CC BY-SA 4.0