I want to express the joint probability of $\Phi_A$ and $\Phi_B$: $p(\Phi_A, \Phi_B)$ conditioned that $\Phi_A$ and $\Phi_B$ are both greater than some value C. How would I express this mathematically? I guess my intuition says:

$p(\Phi_A, \Phi_B | \bf{\Phi} >C)$

Is this correct? Is there a better way to express this?


Well, it is your choice which notation to use, but you certainly can just use logical operators:

$p(\Phi_A, \Phi_B \; |\; \Phi_A>C \,\cap \Phi_B > C)$

Your current notation is not clear as $\Phi$ is not defined and not obvious what it means.


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