do the following, and you will definetely feel a better idle when you start ur car.
1- did you reset the ecu yet when you installed the CAI
? if so, then cool. or else reset it.
2- make sure you installed everything right on the CAI
3- clean ur MAF sensor. common problem is rough idling if MAF is a bit dirty.
4- clean ur throttle body. you will definetely feel improvement when you clean the throttle body. make sure when you clean it, pull the throttle cable so the throttle body opens up and you can clean the inside of it as far as ur hand can reach.
cleaning the throttle body will definetely solve ur problem, but i cant tell you how much it will solve it. cleaning it every 6 months ur throtle body is a good idea.
if ur car still dies while idling, then its ur idle control valve. a 250$ estimate price of part.
good luck, and let us know wut the problem was. while ur at it, make sure ur throttle cable is tight enough