Analyzing Decisions and Strategies with Probability
Statistics and Probability · Flashcards · Application
STATISTICS AND PROBABILITY · FLASHCARDS
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QUESTION
A goalie-pull choice: If pulled, win prob is
0.12
0.12
0.12
; if not, win prob is
0.06
0.06
0.06
. Which strategy maximizes win probability?
QUESTION
What is
E
(
X
)
E(X)
E
(
X
)
if you gain $100 with prob
0.02
0.02
0.02
and lose $5 with prob
0.98
0.98
0.98
?
QUESTION
What is
P
(
D
∣
+
)
P(D\mid +)
P
(
D
∣
+
)
if
P
(
D
)
=
0.50
P(D)=0.50
P
(
D
)
=
0.50
,
P
(
+
∣
D
)
=
0.90
P(+\mid D)=0.90
P
(
+
∣
D
)
=
0.90
, and
P
(
+
∣
D
c
)
=
0.10
P(+\mid D^c)=0.10
P
(
+
∣
D
c
)
=
0.10
?
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ANSWER
0.90
0.90
0.90
. Apply Bayes' theorem:
0.5
(
0.9
)
0.5
(
0.9
)
+
0.5
(
0.1
)
=
0.45
0.5
\frac{0.5(0.9)}{0.5(0.9)+0.5(0.1)}=\frac{0.45}{0.5}
0.5
(
0.9
)
+
0.5
(
0.1
)
0.5
(
0.9
)
=
0.5
0.45
.
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