Suppose we have 3 different trained neural network models that we are considering using for predicting whether a photo (a matrix of 10,000 by 10,000 black/white intensity pixel values) contains a dog or a cat. Each neural network takes a photo as input and outputs a probability for dog and cat respectively. We also have 1000 examples of labeled dogs and cats from the Asirra data set. In addition, we have a new picture (of either a dog or a cat) and we want to know if it is a cat. In the questions below, we are asking you to translate concepts in English into formal nota- tion. You should use notation such that someone knowledgeable about statistical machine learning can tell exactly what your notation specifies with no uncertainty. You do not need to derive solutions or show how to compute an expression. Define the variables and expressions you will need in for the questions below. Which model do we think is best? If we assume that these three models are the only possibilities for how the labels were generated, what do we think is probability that model 1 is the true model? What does that model predict is the probability that the new picture depicts a cat? Without having made a hard choice of model, what do we think is the probability that the new picture depicts a cat