Question#1

A random vector, when resolved along the x and y axes of a rectangular Cartesian coordinate system, has the components X and Y, which are independent Gaussian random variables, each with a zero- mean unity-variance normal distribution N{0, l). ( a) Find the joint probability density function of the two random variables R and (E) which are the magnitude and angle of the vector, dened by R = 0(2 + Yzy/z (E) = tan'1 ( Y I X) (b) Find the marginal probability density function of the random variable R. ( c) Determine whether the random variables R and (E) are also mutually independent