Re: mutually exclusive vs independent

Ethan.Johnsons@xxxxxxxxx wrote:
So, "independent" can have the overlapping area in Veen diagram,
correct?

More than that. They HAVE to overlap in a Venn diagram. If events A and B are independent, p(A) = p(A|B), and p(B) = p(B|A). In other words, knowledge that B has happened does not affect p(A); and knowledge that A has happened does not affect p(B).

In your Venn diagram, if it is drawn to scale:

p(A) = area of circle A over total area
p(B) = area of circle B over total area
p(A|B) = area of A-B intersection over area of circle B
p(B|A) = area of B-A intersection over area of circle A

So, for p(A) to equal p(A|B), and for p(B) to equal p(B|A), there has to be overlap, and it must be in the correct proportions.


Then, what is "dependent"?

Not independent. Related.



thx much

Reef Fish wrote:
Ethan.Johnsons@xxxxxxxxx wrote:
I thought I understood this, but getting back to me again.
Can you pls explain 'mutually exclusive' vs 'independent' for me with
examples if possible?
The simplest mnemonics for the DIFFERENCE between the two concepts is
that THEY are mutually exclusive, i.e., they cannot both happen!

A and B are mutually exclusive if A intersect B is the empty set,
hence
P(A and B) = 0.

If A and B are non-empty events, the they are independent IF and ONLY
IF
P(A and B) = P(A) * P(B)..NE. zero.

-- Reef Fish Bob.



--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.

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