Go Classes | DA Course | Machine Learning

$\text { Consider the following set of training examples: }$

\begin{array}{|l|c|c|c|}
\hline \text { Instance } & \text { Classification } & \mathbf{X}_{\mathbf{1}} & \mathbf{X}_{\mathbf{2}} \\
\hline 1 & + & \mathrm{T} & \mathrm{~T} \\
\hline 2 & + & \mathrm{T} & \mathrm{~T} \\
\hline 3 & - & \mathrm{T} & \mathrm{~F} \\
\hline 4 & - & \mathrm{F} & \mathrm{~F} \\
\hline 5 & - & \mathrm{F} & \mathrm{~T} \\
\hline 6 & - & \mathrm{F} & \mathrm{~F} \\
\hline
\end{array}

What is the information gain of $\mathrm{X}_2$ relative to these training examples ?

1. $\frac{1}{6} \log 3+\frac{1}{3} \log \frac{3}{2}$
    
2. $ \log 3+\\log \frac{3}{2}$
    
3. $\frac{2}{6} \log 3+\frac{2}{3} \log \frac{3}{2}$
    
4. $\frac{1}{6} \log \frac{1}{6}+\frac{1}{3} \log \frac{1}{3}$