Question 5: Suppose we are solving a binary classification task using…

Suppose we are solving a binary classification task using a neural network with the following architecture:

• Input: $x = \begin{bmatrix} 1 \\ 1 \end{bmatrix}$
• Hidden layer: 2 neurons (ReLU activation)
• Output layer: 1 neuron (sigmoid activation)

The weight parameters of the network are given as:

$W^{(1)} = \begin{bmatrix} w_1^{(1)} & w_2^{(1)} \\ w_1^{(2)} & w_2^{(2)} \end{bmatrix} = \begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}, \quad W^{(out)} = \begin{bmatrix} w_1^{(out)} & w_2^{(out)} \end{bmatrix}^T = \begin{bmatrix} 1 & 2 \end{bmatrix}^T,$

where $w_i^{(j)}$ represents the weight associated with the $j$-th neuron for the $i$-th input feature. What are the predicted probabilities?