Can I play PSP games on my PS3?

This is most likely a dumb question, but I thought I'd ask anyway. Can I play PSP games on my PS3? I purchased PSone game (SotN) and you can play that on both the PSP and PS3. If I buy a PSP game, like Dracula X Chronicles, will I also be able to play it on my PS3?

no

Only PS1 games and minis

...and if you own the 60Gb version of PS3, you can play PS2 games on it too.