In a missile-testing program, one random variable of interest is the distance between the point at which the missile lands and the center of the target at which the missile was aimed. If we think of the center of the target as the origin of a coordinate system, we can let X denote the north-south distance between the landing point and the target center and let Y denote the corresponding east-west distance. (Assume that north and east define positive directions.) The distance between the landing point and the target center is then Z=sqrt(X^2+Y^2). X and Y are independent variables, and probability density function of X and Y are as follows:

F_X(x)=2x if 0

F_X(x)=0 otherwise

F_(y)=1 if 0

F_(y)=0 otherwise

(1) Find the cumulative distribution function for Z= sqrt(X^2+Y^2)

(2) Find P[Z>1/2]