Conditional Probability and Independence
Statistics and Probability · Flashcards · Recall
STATISTICS AND PROBABILITY · FLASHCARDS
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QUESTION
What does the notation
P
(
A
∣
B
)
P(A\mid B)
P
(
A
∣
B
)
mean in words?
QUESTION
State the multiplication rule that expresses
P
(
A
∩
B
)
P(A\cap B)
P
(
A
∩
B
)
using
P
(
A
∣
B
)
P(A\mid B)
P
(
A
∣
B
)
and
P
(
B
)
P(B)
P
(
B
)
.
QUESTION
State an equivalent independence condition using only
P
(
A
∩
B
)
P(A\cap B)
P
(
A
∩
B
)
,
P
(
A
)
P(A)
P
(
A
)
, and
P
(
B
)
P(B)
P
(
B
)
.
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ANSWER
A
A
A
and
B
B
B
are independent if
P
(
A
∩
B
)
=
P
(
A
)
P
(
B
)
P(A\cap B)=P(A)P(B)
P
(
A
∩
B
)
=
P
(
A
)
P
(
B
)
. Product rule holds when events don't influence each other.
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