A different level explanation, which may or may not be helpful:

Read up on affine space, convex combinations, and maybe this article about torsors.

If you are frustrated with hand waving in calculus, read a Real Analysis textbook. The magic words which explain how the heck you can have a probability distributions over real numbers is measure theory).

A different level explanation, which may or may not be helpful:

Read up on affine space, convex combinations, and maybe this article about torsors.

If you are frustrated with hand waving in calculus, read a

Real Analysistextbook. The magic words which explain how the heck you can have a probability distributions over real numbers ismeasure theory).