I'm studying the Box Muller transform and I cannot see how Z0 and Z1 represent standard normal distributions. I've looked at the wikipedia page for the box-muller function but they don't seem to have a proof that shows Z0,1 are normally distributed. Does anyone have any ideas about how to go about proving this?
$$Z_2 = R \cos(\Theta) = \sqrt{-2 \ln U_1} \cos(2 \pi U_2). $$ $$Z_1 = R \sin(\Theta) = \sqrt{-2 \ln U_1} \sin(2 \pi U_2). $$ $$ \text{where } U_1,U_2\sim \text{Uniform}(0,1) $$