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My question is the following. Let's say I have two probability distributions;

[tex]f(x|b)\,g(x|c)[/tex]

b and c are discrete events while x is a continuos 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,

[tex]h(x|b,c)\,?[/tex]

And, what assumptions do those strategies rest on?

Thank you in advance,

Will