I have been reading Chapter 4 of Shreve's Stochastic Calculus for Finance II. It is easy to understand the simple process, $\Delta(t)$, defined on Page 126, which is just a constant inside a given subinterval.
Later in the Exercise 4.2 and 4.3, it is mentioned again. The process $\Delta(t)$ is simple and nonrandom in 4.2 while it is simple but random in 4.3.
How should I understand the randomness of such process?
I am just a beginner of financial math. Thanks in advance! Good reference will also be appreciated!