y c- ( 0,1) Q&A – Policies
-Trenn 6CCS3AIN
c -Trenn, King’s College London
1
Pacmanfeelingtheheat roti” %”÷÷
v0
–
v1
v2
v30
vend
v3
v7
v4
v5
v6
%¥5÷¥
Pacman just moves randomly to any adjacent tile excluding the tile he just came from.
If Pacman falls into the lava, then that’s it.
What’s the probability that Pacman survives this?
Say Pacman starts at v0 and wants to go to vend.
There is so much smoke that Pacman cannot see anything.
c -Trenn, King’s College London 2
Pacman feeling the heat
Pp-_ 3-5 471-10 Pg =p -1 2) 11-100
v0 v1 v2 v30 vend p: v3 v7
T.IE?nf.zq,(5′ +551=0.012
v4 v5 v6
” iv. rows
EETit-t.IE?H)–EEEpiIn–&?p–NPyi– ⇒A-¥
c -Trenn, King’s College London
3
ETD=p
I
3) 101-1000
Pacman feeling the heat
E E T ]=EÉiiPCT=i ) PITT)=Ez
pCT=1) = } PITS2)=§
‘ 8+{
¥3
plT=4)=
=¥a
—
p
v→ v 01
v→ v 0 v
2 3 end
→
→
in
d
to
v3
v7
v4
v5
v6
5PCT=i)= / How long does it take Pacman to either end up in the lava or at the end?
time
.fr–
How long does it take until Pacman makes it to the end conditioning on the event
that he didn’t fall into the water.
c -Trenn, King’s College London
4
Pacman feeling the heat
v0
v1
v2
v30
vend
v3
v7
v4
v5
v6
c -Trenn, King’s College London 5
Ten hats
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i gets hit hat bad otherwise
✗i := ✗=
Ten men enter a restaurant. When they come in each of them gives their hat to the receptionist
When they leave the restaurant, each of them gets a random hat back. How many get their own hat back in expectation?
EEE Ei] = ÉEF:] ”
= ¥4,to= I
EEXT
=
c -Trenn, King’s College London
6