Question: Box-Muller method. (10 points) (a) (5 points) Show that for (X, Y ) N (0, I2), if R = X2 + Y 2, and =

Box-Muller method. (10 points) (a) (5 points) Show that for (X, Y ) N (0, I2), if R = X2 + Y 2, and = angle[(X, Y )], then R and are independent. (b) (5 points) Show that unif[0, 2] and random variable R2 exp(2)

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