I am studying Randomized Algorithms chapter in the book "Introduction to Algorithms" by Cormen et al.
In this chapter the book introduces the concept of an indicator random variable and state that the expected value of an indicator random variable as :
I am having difficulty understanding why this is called an indicator random variable, specifically why indicator and random and how this concept is useful in analyzing algorithm timings . It has been some time since I studied probability in school . However , I am aware of the concept behind probability. So you can base your answer on this premise.
As you can see from the diagram all it is saying is that the expected value of an indicator random variable of an event is equal to the probability of that event . We already have the concept of probability , why should we know about this new concept which happens to be the same value as the probability ?