EN
Let L1,L2,...,Ln+1 be the lengths of subintervals created by division of the interval [0,t] by n randomly and independently selected points of this interval. B. de Finetti (1964) proved that F(t;a1,⋯,an+1)=P({L1>a1,⋯,Ln+1>an+1})=t^(−n)(t−a1−...−an+1)^n, where ai≥0,i=1,...,n+1, and a1+...+an+1