Abstract: Let (,,) be a complete probability measure space and X1 and X2 be separable Banach spaces. For Banach spaces Y1 and Y2, let F1: X1Y1 and F2: X2Y2 be random operators. Using F1 and F2, we construct a random operator F: (X1X2)Y1Y2, which is continuous if F1 and F2 are continuous. We prove that if F1 and F2 are stochastically continuous, then F is also stochastically continuous. Similar result is also established in case of separability of random operators. The fixed points of such random operators on the tensor product of Banach spaces is also studied here.