The test for the independence of two events is clearly stated here: http://en.wikipedia.org/wiki/Indepen...ability_theory)
Hi, im just confirming if this logic is right, for my assignment. Well i know that events are mutually exclusive if . And then this is not independent.
so if i wanted to determine is something is independent then is it just if is not equal to 0?
coz in this subject we havent covered stuff like chi-squares so im not allowed to do that. thanks
The test for the independence of two events is clearly stated here: http://en.wikipedia.org/wiki/Indepen...ability_theory)
OMG that's a BAD typo
you mean intersection and not union here.
Another clarification...
Mutually exclusive or disjoint means that the intersection of two sets is empty,
THAT implies that P(AB)=0.
BUT P(AB)=0 does not mean they are disjoint.
Also If two sets are independent then..........
and
and
and
and
and
IF any one hold, ALL HOLD.
And if one fails, they all do.
NOW to the question at hand, which I did in class 2 weeks ago.
IF A and B are disjoint (and they have positive probability) then they are dependent.
That's because P(AB)=0 while P(A)P(B)>0, so
If they are independent
It then follows that too.
You only need show that 2 of these 3 are equal
the other must also be equal to the first two.
These are the more intuitive definitions.
IF A and B are independent then knowing one does not change the probability of the other.