Mutually Exclusive or Disjoint?

[ku]

For two events [math]A_1[/math] and [math]A_2[/math], if [math]A_1 \cap A_2 = \emptyset[/math] then we say that [math]A_1[/math] and [math]A_2[/math] are disjoint. Does disjointedness differ to mutual exclusiveness? Are they both the same or are they different?

[Abd-al-Karim]

For two events and , if then we say that and [/url'] are disjoint. Does disjointedness differ to mutual exclusiveness? Are they both the same or are they different?

 

I have never come accross the term disjoint in statistics/probability theory before but rom you have said it seems to mean the same thing as mutually exclusive. If then the two sets shre not common elements and I guess one could say they are disjoint.

 

However maybe its mean in a graphical sense because in that case it makes more sense. If you can imagine a Venn diagram of events and (each would be represented by a circle) if then the circles do not overlap or touch in any way they are apart and could be said to be disjoint as opposed to: if where and , when i guess they could be said to be joint or joined together because the circles overlap.

 

PS I'm sorry I tried to Google some decent Venn diagrams but could'nt find any relevent ones if it still doesn't make sense let me know and i'll scan some in or something.

[antiphon]

For two events and , if then we say that and [/url'] are disjoint. Does disjointedness differ to mutual exclusiveness? Are they both the same or are they different?

 

They are the same.

 

The term "disjoint" is quite common in measure theory, where arbitrary mathematical sets are considered. "Mutually exclusive" is a heuristic phrase that has no meaning in the case of general measures. Probability measure (i.e. measure with[math]P(\Omega)=1[/math]) gives the sets [math]A\subseteq\Omega[/math] the interpretation of "events", so saying "mutually exclusive events" makes sense.

 

 

Cheers,

 

Tuomas