I'm given the following question;
Consider a renewal process for which the lifetimes X1, X2, · · · are discrete r.v. having the Poisson distribution with mean λ.
And then asked to find the distribution of the Waiting time $W_k$ and P(N(t) = k), using the standard definitions of
\begin{align} & W_k = \sum_{i=1}^k X_i \\ and\\ &N(t) = \sum_{n=1}^\infty \Bbb{I}\{{W_k \leq t}\} \end{align}
Unfortunately, I don't quite understand what is being asked. My understanding of a standard renewal process is that each $X_i$ exists for a certain period of time before failing, and then the next $X_i$ begins. But in this case, I don't see how a sequence of Poisson random variables satisfies this. I think once I actually understand the framing of the question I will be fine, so any assistance on what the question means would be greatly appreciated.