Write a function log$\_$prob that takes the numpy arrays train$\_$features, ${}_y,{}_y,$ and $log{p}_y$ as input, and outputs the following matrix with the shape $(N,2)$ where $N$ is the number of training data points. $x_i$ is the $i^{th}$training data point. Try and avoid the utilization of loops as much as possible. No loops are necessary. stored using the common standards.

In $[23]$: def log$\_$prob$($train$\_$features, mu$\_$y$,$ sigma$\_$y$,$ log$\_$py$)$:

$N,d=$ train$\_$features. shape

# your code here

# Add the log probability of $y$

log$\_$p$\_$x$\_$y $+=$ log$\_$py$.$reshape $(1,-1)$