With the increasing integration of power plants into the frequency-regulation markets, the importance of optimal trading has grown substantially. This paper conducts an in-depth analysis of their optimal trading behavior in sequential day-ahead, intraday, and frequency-regulation markets. We introduce a probabilistic multi-product optimization model, derived through a series of transformation techniques. Additionally, we present two reformulations that re-frame the problem as a mixed-integer linear programming problem with uncertain parameters. Various aspects of the model are thoroughly examined to observe the optimal multi-product trading behavior of hydro power plant assets, along with numerous case studies. Leveraging historical data from Nordic electricity markets, we construct realistic scenarios for the uncertain parameters. Furthermore, we then proposed an algorithm based on the No-U-Turn sampler to provide probability distribution functions of cleared prices in frequency-regulation and day-ahead markets. These distribution functions offer valuable statistical insights into temporal price risks for informed multi-product optimal-trading decisions.