We propose an exploratory form of motor babbling that uses variance predictions from a recurrent neural network as a method to acquire the body dynamics of a robot with flexible joints. In conventional research methods, it is difficult to construct real robots because of the large number of motor babbling motions required. In motor babbling, different motions may be easy or difficult to predict. The variance is large in difficult-to-predict motions, whereas the variance is small in easy-topredict motions. We use a Stochastic Continuous Timescale Recurrent Neural Network to predict the accuracy and variance of motions. Using the proposed method, a robot can explore motions based on variance. To evaluate the proposed method, experiments were conducted in which the robot learns crank turning and door opening/closing tasks after exploring its body dynamics. The results show that the proposed method is capable of efficient motion generation for any given motion tasks.