1
$\begingroup$

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]
```
$\endgroup$

1 Answer 1

4
$\begingroup$

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 *)
$\endgroup$
2
  • $\begingroup$ It's exactly what I was looking for. Thank you, Bob! $\endgroup$
    – WHoZ
    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 $\endgroup$ Sep 30, 2020 at 8:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.