1. in deep learning, a network of neurons is trained to take high-dimensional input x and predict output y. Consider a network trained to predict a Bernoulli experiment, where y {0,1}. In this case, the neural network is just some complicated function p(x) for the probability of success when the input is x. To train the network, you collect a lot of independent observations {(xi, yi) : i = 1, 2, . . . , n} and use them to learn the strength of neural connections. Specifically, the neural connection strengths are adjusted to maximize the probability of the dataPr(y1,y2,...,yn). What is this probability in terms of the notation given in this problem?