Class Activity: Performance estimation and ROC

In a binary classification problem, we have a data set with $200$ positive and $300$ negative examples. After plotting the ROC we observed that the curve goes through the point $TPR=$ FPR $=0\mathrm{.}45.$ Calculate the Precision at this point.

Class Activity: Feature selection by covariance

For the following training dataset:

$\backslash$table$[[$F$1,$F$2,$F$3,$F$4,$Target Value$],[1,2,3\mathrm{.}5,0\mathrm{.}75,1\mathrm{.}5],[2,2,4\mathrm{.}5,-0\mathrm{.}25,1\mathrm{.}5],[3,1,4\mathrm{.}5,1\mathrm{.}75,1],[-1,1,0\mathrm{.}5,1\mathrm{.}75,1],[-2,3,1\mathrm{.}5,4\mathrm{.}75,2],[4,1,5\mathrm{.}5,2\mathrm{.}75,1],[1\mathrm{.}5,2,3\mathrm{.}5,0\mathrm{.}25,1\mathrm{.}5],[3\mathrm{.}25,4,7\mathrm{.}25,0\mathrm{.}5,2\mathrm{.}5]]$

Calculate the Pearson correlation coefficients and select the best two features using the correlation results.