Question: 27. When a dart is thrown at a circular target, consider the location of the landing point relative to the bulls eye. Let X be

27. When a dart is thrown at a circular target, consider the location of the landing point relative to the bull’s eye. Let X be the angle in degrees measured from the horizontal, and assume that X is uniformly distributed on [0, 360].

Define Y to be the transformed variable Y h(X)

(2/360)X , so Y is the angle measured in radians and Y is between and . Obtain E(Y) and Y by first obtaining E(X) and X, and then using the fact that h(X) is a linear function of X.

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