It happens frequently that I find textbook derivation confusing, that some steps have no connection.
For example, when learning the definition of exponential distribution and derivation by modifying poisson distribution:
The exponential distribution with positive parameter λ is given by $$ f(x)=\Bigg\{\begin{array}{c|c} λ e^{-λx} \quad for \; x>0\\ \ 0 \quad\,\,\,\,\,\,\,\,\, for \; x\leq0. \end{array} $$ and satisfies $\int_ {-\infty} ^ \infty \,f(x)\,dx=1$ as required. The exponential distribution occurs naturally if we consider the distribution of the length of intervals between successive events in a Poisson process or, equivalently, the distribution of the interval (i.e. the waiting time) before the first event. If the average number of events per unit interval is $λ$ then on average there are $λx$ events in interval $x$, so that from the Poisson distribution the probability that there will be no events in this interval is given by
$$Pr\;(no\;events\;in\;interval\;x)=e^{-λx}.$$
It takes me a long time to realise that I have to substitute x=0 in poisson distribution to arrive at the final result. To the author this step is obvious enough not to mention it explicitly, but it is not so to me. Why is that? I encounter this kind of frustration frequently and I hope someone who has been through that could enlighten how to avoid getting stuck when reading a textbook.