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Path planning in dynamic environments is essential to high-risk applications such as unmanned aerial vehicles, self-driving cars, and autonomous underwater vehicles. In this paper, we generate collision-free trajectories for a robot within any given environment with temporal and spatial uncertainties caused due to randomly moving obstacles. We use two Poisson distributions to model the movements of obstacles across the generated trajectory of a robot in both space and time to determine the probability of collision with an obstacle. Measures are taken to avoid an obstacle by intelligently manipulating the speed of the robot at space-time intervals where a larger number of obstacles intersect the trajectory of the robot. Our method potentially reduces the use of computationally expensive collision detection libraries. Based on our experiments, there has been a significant improvement over existing methods in terms of safety, accuracy, execution time and computational cost. Our results show a high level of accuracy between the predicted and actual number of collisions with moving obstacles.