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A number line from 0 to 1 is attached at its ends to form a circle. Two spinning arrows are placed in the middle of this circle (see below). The blue arrow is spun once so that it is pointing to a random position on the circumference of the circle, unknown to you. Then, the red arrow is spun, and you are told only whether it lands on a number that is greater or less than the blue arrow; this is repeated several times while the blue arrow remains fixed.
a.) What is the probability density for the position of the blue arrow, given that the red arrow has landed on a greater value H time and a lower value L times?
b.) Give a point estimate for the position of the blue arrow, given that the red arrow has landed on a greater value H time and a lower value L times.