Suppose that X and Y are independent with X N(0, 1) and Y N(0, 4). Let U = X + Y and V = X Y . a) Find the joint probability density function of (U,

Suppose that X and Y are independent with X ∼ N(0, 1) and Y ∼N(0, 4). Let U = X + Y and V = X − Y .

a) Find the joint probability density function of (U, V), fu,v(u, v).

b) Are U and V independent?

c) Sketch the support of (U,V).