A target is a disk of radius 3 feet centered at the origin. A competitor fires a

Question

A target is a disk of radius 3 feet centered at the origin. A competitor fires a projectile at the target and receives 30 points if it lands within 1 foot of the center, 20 points if it lands between 1 and 2 feet of the center, and 10 points if it lands between 2 and 3 feet of the center (and 0 points otherwise). Let (X,Y) represent the coordinates where the projectile hits and let S be the score.
2. Suppose the position of the projectile on the target is a bivariate normal with X and Y independent standard normal with 'rho' = 0.
After finding finding the joint pdf of (R, 'theta'), the polar coordinates of the point where:
R = sqrt(X^2 + Y^2) and 'Theta' = arctan(Y/X) in the previous part:
(d) Find the marginal distributions of R and 'theta' and sketch their graphs (if you can)
(e) Find E[R] and interpret it; Find Var(R) and SD(R), where SD is the standard deviation.

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