Suppose that R and U are independent continuous random variables where U has a Uniform distribution on [0, 1] and R has the density function
![1738_719da2cc-a2dd-4ea7-867e-48332170077a.png](https://secure.tutorsglobe.com/CMSImages/1738_719da2cc-a2dd-4ea7-867e-48332170077a.png)
(a) Show that R2 has an Exponential distribution.
(b) Define X = R cos(2πU) and Y = R sin(2πU). Show that X and Y are independent standard Normal random variables.
(c) Suggest a method for generating Normal random variables based on the results in part (a) and (b).