I have admin and limited user account on my PC. I always run in
limited user account, except when installing program and doing other
system maintenance work.

In limited user account, when I install a program, it will pop up a
dialog to ask for admin password.

Suppose that under limited user account, I by mistake downloaded
virus/trojan, can this virus/trojan/key logger steal the admin
password when I try to install a program?

I know that I'll be safe if I switch to admin account to do the
installation.

And yes, there is a possibility that the virus will change the program
I want to install. Let's ignore this possibility for now.

I am running Win7.

Thanks.