8
The dribble success probability
y
in fact depend on the presence or absence of a defending robot,
D
.
A
has
no way of detecting whether
D
is present, but does know some statistical properties of its environment.
D
is present
2
3
of the time. When
D
is absent,
y
=
3
4
. When
D
is present,
y
=
1
4
.
(f) (4 pt)
What is the posterior probability that
D
is present, given that
A
D
ribbles twice successfully from
1 to 3, then
S
hoots from state 3 and scores.
We can use Bayes’ rule, where
D
is a random variable denoting the presence of
D
, and
e
is the evidence
that
A
dribbled twice and scored.
P
(
d

e
) =
P
(
e

d
)
·
P
(
d
)
P
(
e
)
P
(
e
) =
P
(
e

d
)
·
P
(
d
) +
P
(
e
¬
d
)
·
P
(
¬
d
)
P
(
e

d
) =
1
4
·
1
4
·
1
2
P
(
e
¬
d
) =
3
4
·
3
4
·
1
2
P
(
e
) =
1
32
·
2
3
+
9
32
·
1
3
=
11
96
P
(
d

e
) =
2
96
/
11
96
=
2
11
(g) (3 pt)
What transition model should
A
use in order to correctly compute its maximum expected reward
when it doesn’t know whether or not
D
is present?
To maximize expected total reward, the agent should model the situation as accurately as possible.
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 Spring '08
 Staff
 Artificial Intelligence, Conditional Probability, Probability theory, dribble success probability, successful dribble, successful previous dribble

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