(4) (2 Points) Let U be U(0, 2)-distributed, R be independent of U with distri- bution...

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(4) (2 Points) Let U be U(0, 2)-distributed, R be independent of U with distri- bution function (1 - exp(-r/2) r0, FR(r) = otherwise. Show that (X, Y) := g(R, $), where g is the function given in (3), is N(0, )- distributed with = (69). Also, show that R E[X + Y]. Hint: fre-r/2dr = = X2 Y2 and find (4) (2 Points) Let U be U(0, 2)-distributed, R be independent of U with distri- bution function (1 - exp(-r/2) r0, FR(r) = otherwise. Show that (X, Y) := g(R, $), where g is the function given in (3), is N(0, )- distributed with = (69). Also, show that R E[X + Y]. Hint: fre-r/2dr = = X2 Y2 and find