Problem 4. Sum of Random Variables. In a game of “blindfold darts" (not recommended at home!) a participant throws two darts independently at a circular board of radius R. The landing position of each dart is distributed uniformly over the board (and we assume that they can't miss the board entirely). For each dart's location, the distance from the center is calculated and the participant's score is computed as the sum of these two distances. What is the distribution of the participant's score? You may use results proven in class without re-proving them.

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