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Statistics 400
Lecture 16
Review
Random Variable:
(R.V.) is a variable whose value is a numerical outcome
of a random phenomenon.
Notation
: X, Y, Z
Probability
Theorem 2.11
: Complementary Rule:
P (A
’
) = 1P (A)
Theorem 2.12
: P(
Φ
)=0
Theorem 2.13:
If
B
A
⊂
, P(A)
≤
P(B)
Theorem 2.15
: Addition Rule:
P
(
B
A
∪
)=P(A) + P(B)  P(
B
A
∩
)
Conditional Probability:
the probability of a certain event given that a specific condition is
satisfied.
Assume P (A) > 0
)
(
)
(
)

(
B
P
B
A
P
B
A
P
∩
=
=
)
(
)
(
B
P
AandB
P
Properties of conditional probability:
(A)
1
≥
P(AB)
≥
0
(B)P(BB)=1
(C)If A1, A2, A3,…Ak are mutually exclusive events
P(A1
∪
A2
∪
…
∪
AkB)=P(A1B)+P(A2B)+…+P(AkB)
Definition 2.3.2
P(A
∩
B)=P (A and B) = P(BA) * P (A)
P(A
∩
B)=P (A and B) = P(AB) * P (B)
Ping Ma
Lecture 16
Fall 2005
 1 
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View Full Document Event A and event B are
independent
if
P(A
B)=P(A and B) = P (A) * P (B)
Bayes’ Theorem
P(BA)=
)
(
)
(
A
P
A
B
P
=
)
B'

P(A
*
)
P(B'
B)
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This note was uploaded on 07/24/2008 for the course STAT 400 taught by Professor Tba during the Fall '05 term at University of Illinois at Urbana–Champaign.
 Fall '05
 TBA
 Statistics, Probability

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