Triangular distribution (piecewise PDF and CDF and moments)
TriangularDistribution[{min, max}]
TriangularDistribution[]
TriangularDistribution[{min, max}, c]
PDF[TriangularDistribution[{min, max}, c], x]
→ Piecewise[{{(2*(-min + x))/((-min + max)*(-min + c)), min <= x <= c}, {(2*(max - x))/((-min + max)*(max - c)), Inequality[c, Less, x, LessEqual, max]}}, 0]CDF[TriangularDistribution[{min, max}, c], x]
→ Piecewise[{{(-min + x)^2/((-min + max)*(-min + c)), min <= x <= c}, {1 - (max - x)^2/((-min + max)*(max - c)), Inequality[c, Less, x, LessEqual, max]}, {1, x > max}}, 0]{Mean[TriangularDistribution[{min, max}]], Mean[TriangularDistribution[{min, max}, c]]}
→ {(max + min)/2, (c + max + min)/3}