Density of a uniform squared

XX is uniform on [0,1][0,1] and Y=X2Y = X^2. Derive the density fYf_Y of YY and evaluate it at y=14y = \tfrac14.

Show hints (2)+
  1. Find F_Y(y) = P(X ≤ √y), then differentiate.
  2. At y = 1/4 you have √y = 1/2.

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Asked at: Jane Street, Citadel

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