Module 6: Independence

Question 1

what does it mean that two events are independence?

Answer 1

the probability of one has nothing to do with the probability of the other occurring.

Ex.
If A and B are independent events. Then:
P(A ∩ B) = P(A)P(B)
P(A|B) = P(A)
P(B|A) = P(B)

Question 2

what is the difference b/w disjoint events and independent events?

Answer 2

independent events do not influence each other while disjoint events, cannot happen at the same time. If one event happens, the other cannot.

Disjoint: Rolling a die and getting a 2 or a 5. You can’t roll both numbers on the same roll, so these events are disjoint.

Independent: Flipping a coin and rolling a die. Whether you get heads or tails on the coin doesn’t affect what number shows up on the die. These events are independent.

Question 3

what is the def of a collection of independent events?

Answer 3

PRODUCT(P(A_i)) where all events in the product are pairwise disjoint.

Also satisfies the follows conditions:
All A_i but we independent from each other on a one - one basis and on a group basis

Question 4

what is the difference b/w disjoint events and pairwise disjoint events?

Answer 4

Disjoint (mutually exclusive) refers to two events that cannot occur at the same time.

Pairwise disjoint refers to a set of multiple events where no pair of events can occur at the same time.

Question 5

does pairwise independence imply independence?

Answer 5

no, see Ex.5