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Is it possible to set something like this? A probability distribution with random parameters

p = BetaDistribution[1, 1]
count = BinomialDistribution[10, p]

(* and to calculate stuff like: *)
Expectation[count]
Probability[count == 3 \[Conditioned] p > 1/2]
```
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The probability distribution for count is

dist = ParameterMixtureDistribution[
  BinomialDistribution[10, p],
  p \[Distributed] BetaDistribution[1, 1]]

(* BetaBinomialDistribution[1, 1, 10] *)

The expected value of count is the Mean of dist

Mean[dist]

(* 5 *)

Probability[count > 1/2, count \[Distributed] dist]

(* 10/11 *)
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2
  • $\begingroup$ It's exactly what I was looking for. Thank you, Bob! $\endgroup$
    – WHoZ
    Commented Sep 30, 2020 at 1:56
  • 1
    $\begingroup$ @WHoZ if you need to draw samples from both distributions, you may also be interested in the resource function ConditionalProductDistribution $\endgroup$
    – Sjoerd Smit
    Commented Sep 30, 2020 at 8:08

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