(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An email is sent on the network in which the recipients (0,1,2,3,4,5} are in communication.

1 can send to 4 and 2

2 to 1,3,5

3 to 0,2,5

4 to 1, 5

5 to 0,2,4

0 to 3 and 5

If a message is sent to 2,3,4,5 it is forwarded randomly to a neighbour (even if this means a repeat). 0 and 1 never forward messages.

Let e_{k}be the expected number of time that a message starting at k is passed on.

Find e_{4}.

2. Relevant equations

E(X) = [tex]\sum[/tex] E(X|A)P(A)

3. The attempt at a solution

I think I need to partition this but I'm unsure on the partition.

Let X be the number of times a message is sent on

E(X) = E(X|1st move is to 0)P(1st move is to ) + E(X|1st move is to 1)P(1st move is to 1) + E(X|1st move is to 2)P(1st move is to 2) + E(X|1st move is to 3)P(1st move is to 3) + E(X|1st move is to 4)P(1st move is to 4) + E(X|1st move is to 5)P(1st move is to 5)

I'm not sure how I'd work these out using a general k to start at.

If I assume I start at 4, as I'm trying to find e_{4}then I get

e_{4}= 0 + 1x(1/2) + 0 + 0 + e_{5}(1/2)

2e_{4}= 1 + e_{5}

e_{5}= 1x(1/2) + 0 + e_{2}(1/3) + 0 + e_{4}(1/3)

I don't really think I'm going about this the right way, I would have thought I need to find a formula for starting at a general k but I don't know how.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Conditional expectation

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**