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Let S be a semicircle of unit radius on a diameter D. A point P is...

  1. Let S be a semicircle of unit radius on a diameter D.
    1. A point P is picked at random on D. If X is the distance from P to S along the perpendicular to D, show that E[X] = π/4.
    2. A point Q is picked at random on S. If Y is the perpendicular distance from Q to D, show that E[Y ] = 2/π.
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