My question is the following. Let's say I have two probability distributions:
$b$ and $c$ are discrete events while $x$ is a continuous variable, i.e., when the button b is pressed there is some distribution for the amount of rain fall the next day, $x$.
When the button $c$ is pressed there is a different distribution of rain fall the next day, $x$. Are there any strategies for estimating the distribution of rain fall if both buttons are pressed, i.e.,
And, what assumptions do those strategies rest on?