If I had to point out a good beginner issue, it would be this one:
Autodifferentiation is a pretty neat and prevalent feature in Julia, and one way to learn what it is would be to contribute. This issue theoretically could work with just a few typing changes. It’s the kind of thing where everyone notices that it would be easy, lots of people seem to want it, but no one has done it yet .
As for something more directly related to Stats (though autodifferentiation is used everywhere!), check out Distributions.jl. They have a bunch of issues tagged as new functions and distributions to implement that are up for grabs.
Some work in MultivariateStats.jl is up for grabs. It’s a small but very useful library. Small makes it easy to jump into:
In general, looking at JuliaStats is probably a good idea for your interests.