I am new to C++ and extremely surprised by the lack of accessible, common probability manipulation tools (i.e. the lack of things in Boost and the standard library). I\'ve d
As mentioned, you'll want to look at boost/math/distributions and friends to meet your needs.
Here's a very good, detailed tutorial on getting these working for you in Boost. You may also want to throw your weight behind stan as well, which looks quite promising within this space.