In a missile-testing program, one random variable of

QUESTION:

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 \(Y_{1}\) denote the north-south distance between the landing point and the target center and let \(Y_{2}\) 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 \(U=\sqrt{Y_{1}^{2}+Y_{2}^{2}}\) . If \(Y_{1} \text { and } Y_{2}\) are independent, standard normal random variables, find the probability density function for \(U\).

Equation Transcription:

Text Transcription:

Y_1

Y_2

U=\sqrt Y_1^2+Y_2^2

Y_1 and Y_2

U