The ability to generate and recognize sequential data is fundamental for autonomous systems operating in dynamic environments. Inspired by the key principles of the brain-predictive coding and the Bayesian brain-we propose a novel stochastic Recurrent Neural Network with Parametric Biases (RNNPB). The proposed model incorporates stochasticity into the latent space using the reparameterization trick used in variational autoencoders. This approach enables the model to learn probabilistic representations of multidimensional sequences, capturing uncertainty and enhancing robustness against overfitting. We tested the proposed model on a robotic motion dataset to assess its performance in generating and recognizing temporal patterns. The experimental results showed that the stochastic RNNPB model outperformed its deterministic counterpart in generating and recognizing motion sequences. The results highlighted the proposed model's capability to quantify and adjust uncertainty during both learning and inference. The stochasticity resulted in a continuous latent space representation, facilitating stable motion generation and enhanced generalization when recognizing novel sequences. Our approach provides a biologically inspired framework for modeling temporal patterns and advances the development of robust and adaptable systems in artificial intelligence and robotics.