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Dependencies between two probability sample spaces OmegaA, OmegaB

  1. Nov 12, 2011 #1
    Suppose you have two sample spaces [itex]\Omega_A[/itex] and [itex]\Omega_B[/itex]. First space contain two outcomes A and A', where A = [itex]\Omega_A[/itex] - A', i.e. the opposite outcomes.

    Second space also contains two opposite outcomes B = [itex]\Omega_B[/itex] - B'.

    Now, suppose that there are dependencies between A, A' and B, B' like below:
    A [itex]\rightarrow[/itex] B'
    A'[itex]\rightarrow[/itex] B v B' (logical alternative)
    B [itex]\rightarrow[/itex] A'
    B'[itex]\rightarrow[/itex] A v A' (logical alternative)

    So, occurrence of non-negative (i.e. A or B) event excludes such (i.e. non negative) event in the other space. Occurrence of a negative event (A' or B') does not imply anything in the other space. So the two "logical alternative" implications could be in fact skipped:
    A [itex]\rightarrow[/itex] B'
    B [itex]\rightarrow[/itex] A'

    My question:
    - how to approach this?
    - is this covered in some math topic?

    Best Regards,
  2. jcsd
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