This work presents a real-time implementation of a cognitive radar system that predicts and avoids interference using a stochastic model of radio frequency (RF) activity. Next-generation radar/radio systems must sense, predict, and avoid interference as the spectrum grows more crowded. The tested cognitive radar monitors the RF environment to estimate the stochastic model parameters followed by a prediction and avoidance stage. An alternating renewal process models RF activity with random busy and idle time distributions, which are used to obtain interference probabilities. These interference probabilities determine a radar transmit bandwidth and center frequency to avoid colliding with other emitters in the environment. The approach is evaluated in terms of collisions and missed opportunities on a set of simulated and real measured RF spectra. Additionally, this paper outlines the effects and complexity of utilizing different distributions, parameters, and modes of operation for the implemented radar system. The results suggest that this approach accurately predicts and avoids RF interference with a degradation in performance as model variance increases.