How do these two processes, finding the expected value of a discrete random variable and finding the dot product
of two vectors, compare?

We can conclude that on this case we have identical processes but excersise 17 use another way to present the probability distribution and as we can see the expected value can be viewed as a dot product of two vectors with one vector containing the outcomes and the other the probabilities for each possible outcome.

Step-by-step explanation:

Assuming this previous info:

Exercise 17. Suppose that we convert the table on the previous page displaying the discrete distribution for the number of heads  occurring when two coins are flipped to two vectors.

Let vector