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Libniz

  • 3 years ago

how are disjoint and independent different

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  1. Zarkon
    • 3 years ago
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    Two events A and B are disjoint if \(A\cap B=\emptyset\) A and B are independent if \(P(A\cap B)=P(A)\times P(B)\)

  2. Libniz
    • 3 years ago
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    thanks

  3. Libniz
    • 3 years ago
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    so if A and B were disjoint P(A U B)= P(A)+P(B) ?

  4. Zarkon
    • 3 years ago
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    another way to look at it if A and B are disjoint...then if I know event A occurs then that means that B cannot occur..thus A and B are dependent (provided their individual probabilities are nonzero)

  5. Zarkon
    • 3 years ago
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    yes

  6. Libniz
    • 3 years ago
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    I will remember that" when it is disjoint it is not independet"

  7. Zarkon
    • 3 years ago
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    correct...provided the nonzero probabilities

  8. Libniz
    • 3 years ago
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    ok

  9. Zarkon
    • 3 years ago
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    since if P(A)=0 then \(P(A\cap B)=0\) and thus \[0=P(A\cap B)=P(A)\times P(B)=0\times P(B)=0\]

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