I am a film-maker and want to know hot to get Hollywood studios,
production companies, and producers to view my work so they can hire
me to direct movies for them.

Online exposure is one way to be "discovered." Here's the story of the
makers of "405," who have attracted a great deal of attention to their
filmmaking skills with a short film that cost only $300:

http://www.strange-engine.com/media_usatoday.asp

Here you will find a good list of links to sites where you can submit
short films:

http://www.indiebin.com/resources/online.shtml

As you may know, NYU, USC and zillions of other universities are
graduating filmmakers every year to say nothing of hugely talented
filmmakers who have never gone to school for filmmaking.  You have to
get your work seen in a venue that creates talk about you and your
work. There are legions of stories of filmmakers who have somehow
gotten their work before an audience and ended up at Sundance or the
one of the film festivals. Hollywood will not come looking for you. 
The other way to get there is to try and get a job any kind of job
with a production company and work yourself up to becoming an
assistant director (AD) on a film of any kind-that puts you in the mix
and you will find out how difficult it is to get "seen" on the other
hand it can put you in the middle of the business of filmmaking. 
There is no one way to get Hollywood to notice you except HARD WORK
AND A COMMITMENT TO DO THE WORK UNTIL THEY NOTICE YOU§