Convert a PAC-learning algorithm into another one which requires no knowledge of the parameter

This is part of a problem in the book Foundations of Machine Learning(page 28). You can refer to chapter 2 for the notations. Consider a family of concept classes $\left\{\mathcal{C}_{s}\right\}_{s}$ where $\mathcal{C}_{s}$ is the set of concepts in $\mathcal{C}$ with size at most $s .$ Suppose we have a PAC-learning algorithm $\mathcal{A}$ that can be…

Why we multiply probabilities with support to obtain Q-values in Distributional C51 algorithm?

In ‘Deep Reinforcement Learning Hands-On’ book and chapter about Distributional C51 algorithm I’m reading, that to obtain Q-values from the distribution I need to calculate the weighted sum of the normalized distribution and atom’s values. Why I have to multiply that distribution with support? How does it work and what happening there?