Consider:

… where \(X, P\) are random variables. Then:

The distribution of \(X\) is * only dependant on the expectation of* \(P\).

Another way to see this:

So, random probabilities, random hazard rates or ‘random effects’ across groups which can only have one success/failure are probably meaningless to talk about.

## 2019

### Random Stuff

## Random Stuff

### Stochastic Bernoulli Probabilities

Consider: