= 42. Let (Xr:r 1} be independent exponential random variables with parameter >, and set Sn Er-1 Xr. Show that: (a) Yk = Sk/Sn, 1 ≤ k ≤ n - 1, have the same distribution as the order statistics of independent variables {Uk: 1 ≤k ≤n-1} which are uniformly distributed on (0, 1), (b) Zk = Xk/Sn, 1 ≤ k ≤n, have the same joint distribution as the coordinates of a point (U₁...., Un) chosen uniformly at random on the simplex Σr=1 ur = 1, ur ≥ 0 for all r.

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