probability distribution
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namely, probability distribution means “a list distributing a tiny little bit of probability value to each possible options”, and it looks somewhat like the following:
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with a set of state \(S\) and a set of actions \(A\), the set \(S \times A\) refers to a set of 2-tuples \((s_t,a_t)\) where \(s_t \in S, a_t \in A\), enumerating all configurations, with the semantic of all possible interaction of agent with the environemnt
the notion of time spent in a subset of this set in here could be formulated as probability distribution of each interaction happening