(1) In this problem, you are tested for the understanding of the structure of a neural network. Note that you are only tested for the model building part, not for the model solving part. Given a house price estimation problem, you are asked to build a simple neural network model that can be used to model and estimate house price. Each house is characterised by three features, i.e., house size, school zone rating and building year. Use vector of [X] = [21, X2, x3]' to represent the house features and [Y] = [y] to represent house price. The neural networkk is essentially a regression model of f: R2 + R. 1. You are asked to build a neural work with only one hidden layer of 2 nodes, using Sigmoid as the activation function. Could you draw a graph to show the structure of your neural network model. Please include the intercepts for the input layer and hidden layer. 2. What is the total number of parameters in your model that needs to be learned from data? 3. Could you write a 'full' mathematical expression for the neural network model you build in 1? By full, I mean write an end-to-end model that evaluate Y using X, you can either write it in one long equation between Y and X directly, or write it in separate equations that defined an embedded function. Refer to slides 24 and 25. If you use separate equations, use a and az as the value of the hidden layer (center layer). You can either define a single parameter for each weight parameter, or put the weight parameters in vector or matrix form with clear definition of the vector or matrix, including its dimension. (1) In this problem, you are tested for the understanding of the structure of a neural network. Note that you are only tested for the model building part, not for the model solving part. Given a house price estimation problem, you are asked to build a simple neural network model that can be used to model and estimate house price. Each house is characterised by three features, i.e., house size, school zone rating and building year. Use vector of [X] = [21, X2, x3]' to represent the house features and [Y] = [y] to represent house price. The neural networkk is essentially a regression model of f: R2 + R. 1. You are asked to build a neural work with only one hidden layer of 2 nodes, using Sigmoid as the activation function. Could you draw a graph to show the structure of your neural network model. Please include the intercepts for the input layer and hidden layer. 2. What is the total number of parameters in your model that needs to be learned from data? 3. Could you write a 'full' mathematical expression for the neural network model you build in 1? By full, I mean write an end-to-end model that evaluate Y using X, you can either write it in one long equation between Y and X directly, or write it in separate equations that defined an embedded function. Refer to slides 24 and 25. If you use separate equations, use a and az as the value of the hidden layer (center layer). You can either define a single parameter for each weight parameter, or put the weight parameters in vector or matrix form with clear definition of the vector or matrix, including its dimension