A point is chosen uniformly at random from a disk of radius 1, centered at the...

A point is chosen uniformly at random from a disk of radius 1, centered at the origin. Let R be the distance of the point from the origin, and Θ the angle, measured in radians, counterclockwise with respect to the x-axis, of the line connecting the origin to the point.

1. Find the joint distribution function of (R,Θ); i.e. find F(r,θ) = P(R ≤ r, Θ ≤ θ).

2. Are R and Θ independent? Explain your answer.

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Expert Solution

milcah answered 7 months ago

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