In this problem, we will linearly approximate the value of a state in a task given different kinds of feature representation. Notice that the weights for features will be given.

Suppose we have a robot navigating in a hallway, as seen in the figure. The robot is trying to navigate to the goal. The robot's current state $($xy location $(x,y))$ is given according

to the coordinate frame in the figure.

Now we would like to use tile coding as our feature representation. Suppose we construct tile codings as shown in the figure below for this navigation task. Here we use the cross

to represent the location of the robot.

$.$

Tilit

For all $6$ tilings, we are given weights for each tiles which define the approximate state value function. Using this approximation scheme, what will be the value of the state

representing the robot's location as shown above?

Compute it up to two decimal places.