Let r1, r2, . . . , rn be uniform random numbers. Define xi ln ri and yi ln (1  ri), for i 1, 2, . . . , n, and z 

n i1 xi. Label each of the following statements as true or false, and then justify your answer.

(a) The numbers x1, x2, . . . , xn and y1, y2, . . . , yn are random observations from the same exponential distribution.

(b) The average of x1, x2, . . . , xn is equal to the average of y1, y2, . . . , yn.

(c) z is a random observation from an Erlang (gamma) distribution.