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Density of a sum of two uniforms

MediumProbabilityRandom Variables~5m

X,YX,Y are independent uniform [0,1][0,1] and S=X+YS = X+Y. Derive the density fSf_S of the sum and evaluate it at s=0.4s = 0.4.

Show hints (2)+
  1. Convolve the two uniform densities.
  2. On 0 ≤ s ≤ 1 the triangular density equals s.

Answer

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0.4

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Asked at: DRW, Two Sigma

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