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