Java Generator for Poisson and Uniform Distributions?

Question

From what I understand, the standard generator is for the Normal Distribution. I have to generate random numbers according to the Normal, Uniform and Poisson Distributions,

Answer 1

Actually, the standard generator is for the uniform distribution. The basic random number generator in any language/library will always (in all cases I know of) use the uniform distribution because that's what comes out of all the popular pseudorandom number generator algorithms - basically, uniform random numbers are the easiest.

I see Eddie already pointed you to a link for other distributions so I'll skip writing the rest of this...