The question and answer below is related to the renewal process. I'm curious how the "I" changed to "H(T)" as indicated by the yellow boxes. Thanks for spending the time to look over my newbie question!
Question

Answer

The question and answer below is related to the renewal process. I'm curious how the "I" changed to "H(T)" as indicated by the yellow boxes. Thanks for spending the time to look over my newbie question!
Question

Answer

By definition, the distribution $H(t)$ of the random variable $X$ is simply $\mathbb{P}(X < t)$. So, the indicator random variable $I$ is $1$ with probability $p = \mathbb{P}(X