I read many threats about collatz here - so dont worry, this is no attempt to any proof, just asking about a curious fact:

This graph gives the stopping-time of collatz-sequences up to $n=10^8$ (source: http://en.wikipedia.org/wiki/File:CollatzStatistic100million.png ) and it's distribution looks very similar to a Poisson distribution.

Is there some known reason why the collatz-sequence stopping time behaves like a poissonian distribution?

What are the connections to other mathematical problems: Does the collatz-conjecture imply other conjectures, or do other conjectures imply the collatz-conjecture?

Thank you!