Question: A question about continue random variable: The point on a straight shortline that is the closest to an offshore lighthouse is called O . Call

A question about continue random variable:

The point on a straight shortline that is the closest to an offshore lighthouse is called O. Call this minimum distance L. The lamp in the lighthouse is a double beacon (that is, illumination is provided by two lamps facing in opposite directions). At each instant of time, one spot on the shoreline is illuminated by this lighthouse and as time progresses, the illuminated spot progresses from the point (all the way west) to the point + (all the way east). At a randomly selected time, the distance between the illuminated spot, S, and O is measured and a sign given to it depending on whether the spot is west () or east (+) of O. If the beacon rotates at a constant rate, what is the density function fS(s) of the random variable S. What is the expected value of S?

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