An archery target is made of 3 concentric circles of radii 1/ √ 3, 1 and √ 3 feet. Arrows striking within the inner circle are awarded 4 points, arrows within the middle ring are awarded 3 points, and arrows within the outer ring are awarded 2 points. Shots outside the target are awarded 0 points. Consider a random variable X, the distance of the strike from the center (in feet), and let the probability density function of X be f(x) =    2 π(1+x 2 ) x > 0 0 otherwise What is the expected value of the score of a single strike?