Let \(A\) and \(B\) be independent events and let \(\mathbf{1}_A\) and \(\mathbf{1}_B\) be the associated indicator functions. Answer the following questions in terms of \(\mathbf{P}(A)\) and \(\mathbf{P}(B)\).

1. Describe the distribution of \( \mathbf{1}_A\).
2. What is \(\mathbf{E} \mathbf{1}_A\) ?
3. Describe the distribution of \((\mathbf{1}_A +\mathbf{1}_B)^2\).
4. What is \(\mathbf{E}(\mathbf{1}_A +\mathbf{1}_B)^2 \) ?