Exercise: Calculating Likelihood

$\begin{array}{rl}P(y=1\mid \mathbf{x},\mathbf{w})& =\sigma ({\mathbf{w}}^T\mathbf{x}+b)=\frac{1}{1+e^{-({\mathbf{w}}^T\mathbf{x}+b)}}\\ P(y=0\mid \mathbf{x},\mathbf{w})& =1-\sigma ({\mathbf{w}}^T\mathbf{x}+b)\end{array}$

$\mathcal{L}(\mathbf{w})=\prod _{i=1}^n\{\begin{array}{l}P(y=1\mid {\mathbf{x}}_{\mathbf{i}},\mathbf{w}),\text{if }{y}_i=1\\ P(y=0\mid {\mathbf{x}}_{\mathbf{i}},\mathbf{w}),\text{if }{y}_i=0\end{array}$

$\mathcal{L}(\mathbf{w})=\prod _{i=1}^{n}P(y=1\mid {\mathbf{x}}_{\mathbf{i}},\mathbf{w}{)}^{y_i}\times P(y=0\mid {\mathbf{x}}_{\mathbf{i}},\mathbf{w}{)}^{1-y_i}$

$\mathcal{LL}(\mathbf{w})=\sum _{i=1}^n{y}_i\log P(y=1\mid {\mathbf{x}}_{\mathbf{i}},\mathbf{w})+(1-y_i)\log P(y=0\mid {\mathbf{x}}_{\mathbf{i}},\mathbf{w})$

Calculate the likelihood and the log likelihood for the following data set: