Problem 1 (4 pts) The standard Normal distribution: f(x) = 1 _exp{- x /2} V 2t does not have a closed form quantile function, so it would be difficult to apply the inversion method. Instead, we can use a transformation method that still only uses U(0, 1) random variables. Part (a) (1 pt) Consider two independent standard Normal variables X and Y. We can think of these as points on a Cartesian plane: xy