Question

Statistic, Definition of Independent
1) P(A|B) = P(A)
2) P(B|A) = P(B)
3) P(A Union B) = P(A)*P(B)

explain why definition 3 is true for proving cases of independent

Answer 1

are you asking if that is true or false?

Answer 2

3) P(A Union B) = P(A)*P(B) is not true assuming A and B are independent

Answer 3

hmmm, I got these definition off a textbook and is wondering why P(A)*P(B) resulting in proving the set function is independent.
Further explanation please.

Answer 4

The definition is really

\[\Large P(A \cap B) = P(A)*P(B)\]

Answer 5

Notice how I used an intersection symbol and NOT a union symbol

Answer 6

Omg, you're right.
What I meant is intersect!

Answer 7

It turns out that

\[\Large P(A \cap B) = P(A)*P(B|A)\]

assuming A and B aren't independent. However, notice how that if A and B were independent, then

P(B|A) = P(B)

which leads us back to

\[\Large P(A \cap B) = P(A)*P(B)\]

Answer 8

you can do the same form of argument to go from

\[\Large P(A \cap B) = P(A|B)*P(B)\]

to

\[\Large P(A \cap B) = P(A)*P(B)\]

if A and B were independent