As aked this does not make sense:
Can Iset up a RAID of 150 GB velociraptors for performance.
Yes. Trivially easy. And it can be done both in software or with hardware. For max performance you probaly want stripe/RAID1.
(AND RAID 0, RAID 1 and combination like RAID10 work fine without huge CPU loads.)
and then make it so where they automatically back up to a larger
say 2TB western digital caviar black drive?
Uhm no. Or no and yes.
No because RAID is not a backup.
You can however do the following:
First create an array of 10x 150GiB raptors (fast but insane to use that many drives that way).
Then create a mirror of the fast array and the big disk.
This will not backup. This will write a copy of the data to both the fast disks and the backup disk. Thus coming close to what I guess you want to archive.
However depending on your actualy implementation the setup may very well wait until data has been written to both the fast array and the big disk, thus making it as slow as the big disk. And reads might be equally distributed (meaning half the reads may come from the slow disk).
Note that you can still create a very nice fast array with the Raptops. E.g. in a stripe, or a RAID10. And you can backup (as in, actual backup tools) the data. Just do not try to use RAID as backup. Instead rsync daily.