In this paper, we study a remote monitoring system where a receiver observes a remote binary Markov source and decides whether to sample and transmit the state through a randomly delayed channel. We adopt uncertainty of information (UoI), defined as the entropy conditional on past observations at the receiver, as a metric of value of information, in contrast to the traditional state-agnostic nonlinear age of information (AoI) penalty functions. To address the limitations of prior UoI research that assumes one-time-slot delays, we extend our analysis to scenarios with random delays. We model the problem as a partially observable Markov decision process (POMDP) problem and simplify it to a semi-Markov decision process (SMDP) by introducing the belief state. We propose two algorithms: A globally optimal bisection relative value iteration (bisec-RVI) algorithm and a computationally efficient sub-optimal index-based threshold algorithm to solve the long-term average UoI minimization problem. Numerical simulations demonstrate that our sampling policies surpass traditional zero wait and AoI-optimal policies, particularly under conditions of large delay, with the sub-optimal policy nearly matching the performance of the optimal one.