When Bob throws a dart the coordinates of the landing point are a Gaussian pair of independent random variables (X, Y) with zero mean and variance 1. When Rick throws the dart the coordinates are also a Gaussian independent pair but with zero mean and variance 4. Bob and Rick are asked to draw a circle centered about the origin with the inner disk assigned to Bob and the outer ring assigned to Rick. (a) Whenever either player lands on the other player's area, he must pay a $1 to the house. Find the disk radius that minimizes the players' average cost. (b) Repeat part a if Bob must pay $2 when he lands in Rick's area