A dart board is positioned on the disk r+ y 4. A robot is randomly throwing...

 

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A dart board is positioned on the disk r+ y 4. A robot is randomly throwing darts at the board with a probability density function of D(x, y) = K(4-x - y). (a) Find the value of K which normalizes the function (i.e. makes a valid probability density function). (b) Find the probability the robot will throw the dart so that it lands within 1 unit of the bullseye (at the origin). A dart board is positioned on the disk r+ y 4. A robot is randomly throwing darts at the board with a probability density function of D(x, y) = K(4-x - y). (a) Find the value of K which normalizes the function (i.e. makes a valid probability density function). (b) Find the probability the robot will throw the dart so that it lands within 1 unit of the bullseye (at the origin).