Query Plans on Slaves

Hi all!

We're working on our architecture for our next set of systems, and we
normally have a simple master/slave with wal shipping and hot_standby set
up, with pgpool sitting in front of both to do load balancing.

However, one piece I'm very confused about is the query plans on the slave
server.

Let's pretend we have a master server with:
(2) E5-2660 CPU's
(4) S3700 400GB SSD's
256GB of RAM

And multiple slave servers that looks like:
(1) E3-1290 CPU's
(2) Intel 520 SSD's
32GB of RAM

There's a significant difference between the master and slaves.

Does the ANALYZE command run on each system, and work differently on each
system, or would the slave servers use the query plans from the master
machine?

Thanks!

--
Anthony