If I understand your question correctly, then yes.

We use Poisson regression to model the count: For example, number of diseases cases in a region, number of suicides in a country ....

There are a lot of documents online regarding to Poisson regression and how to apply it.

One of those source is:

http://www.ats.ucla.edu/stat/r/dae/poissonreg.htm

but Poisson distribution id for independent events and i am asking for dependent discreet events. can we apply to find out probability for dependent discreet event occurence

#Sadia Bahar.

Now I understand your question better.

You mean "dependent observations" or "dependent events", right?

Because when you wrote "dependent variable", I though you meant the response in a model.