U n 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 Y1 denote the northsouth distance between the landing point and the target center and let. Y2 denote the corresponding eastwest distance. (Assume that. north and east dene positive directions.) The distance between the landing point and the target center is then U = fl/12 -|- 3722. If Y1 and Y; are independent} standard normal random variables, nd the probability density function for U. {10 marks)