Answer to Question #334016 in Statistics and Probability for Dinor123

Question

a) A bivariate continuous random variable (U, V ) has join density function g(u, v), where −∞ <

u, v < ∞. If X = U − V and Y = V + U, show that the joint density function of X and Y is given by

f(x, y) = 1/2 g (x − y/2 , x + y/2) ,

and state a form of this result when U and V are independent.

(b) Suppose U and V are independent random variables with common uniform distribution over the interval [θ −1/4, θ +1/4]. Let X = U −V and Y = U +V . Find the joint density function of (X, Y ).

Hence find the marginal of X and Y .

Answer 1

It's been a while since this question is posted here. Still, the answer hasn't been got. Consider converting this question to a fully qualified assignment, and we will try to assist. Please click the link below to proceed: Submit order