Deep learning has greatly improved visual recognition in recent years. However, recent research has shown that there exist many adversarial examples that can negatively impact the performance of such an architecture. This paper focuses on detecting those adversarial examples by analyzing whether they come from the same distribution as the normal examples. Instead of directly training a deep neural network to detect adversarials, a much simpler approach was proposed based on statistics on outputs from convolutional layers. A cascade classifier was designed to efficiently detect adversarials. Furthermore, trained from one particular adversarial generating mechanism, the resulting classifier can successfully detect adversarials from a completely different mechanism as well. The resulting classifier is non-subdifferentiable, hence creates a difficulty for adversaries to attack by using the gradient of the classifier. After detecting adversarial examples, we show that many of them can be recovered by simply performing a small average filter on the image. Those findings should lead to more insights about the classification mechanisms in deep convolutional neural networks.