A point is generated at random in the plane according to the following polar scheme A radius R is chosen, where the distribution of R2 is X2 with 2 degrees of freedom Independently, an angle is chosen, where uniform(0, 2) Find the joint distribution of X R cos and Y R sin

Question: A point is generated at random in the plane according to the following polar scheme. A radius R is chosen, where the distribution of R2

A point is generated at random in the plane according to the following polar scheme. A radius R is chosen, where the of R2 is X2 with 2 degrees of freedom. Independently, an angle θ is chosen, where θ ~ uniform(0, 2π). Find the joint of X = R cos θ and Y = R sin θ.

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