I read many threads about Collatz here - so don't 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 $n=10^8$ Collatz stopping-time http://upload.wikimedia.org/wikipedia/commons/2/26/CollatzStatistic100million.png (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!