3Note that the sum of two uniform distributions is not a uniform but a Irwin-Hall,
∀n > 1, P([∑
i=1n(Xi ∈ U(0, 1))] = x) ∝
∑
k=0n(-1)k(n
k)
max ((x - k)n-1, 0), converging
towards a Gaussian (central limit theorem).
3Note that the sum of two uniform distributions is not a uniform but a Irwin-Hall,
∀n > 1, P([∑
i=1n(Xi ∈ U(0, 1))] = x) ∝ ∑
k=0n(-1)k(n
k)
max ((x - k)n-1, 0), converging
towards a Gaussian (central limit theorem).