Nonuniform PRNG?

[David Lowry-Duda]

Inspired by the recent thread about pseudorandom number generators on 
python-ideas (where I also mistakenly first wrote this message), I began 
to wonder: suppose that I had a pseudorandom number generator that 
attempted to generate a nonuniform distribution. Suppose for instance 
that it was to generate a 0 bit 2/3 of the time, and a 1 bit 1/3 of the 
time.

How would one go about testing this PRNG against an idealized (similarly 
biased) PRNG?

- DLD