Means of random variables can be thought of as centers of mass. If the random variable is continuous, think of the region under the graph of its probability density function (PDF) as a thin sheet of metal with constant density. The mean will be at the center of mass
Where do we begin? Assuming the reader’s knowledge of the fundamentals of (calculus-based) probability theory, the best place to start is with continuous survival models. This is also a common initial chapter in the textbooks on the subject.