Let r₁, r₂, . . . , r_n be uniform random numbers. Define x_i = − ln r_i and y_i = − ln (1 − r_i), for i = 1, 2, . . . , n, and Label each of the following statements as true or false, and then justify your answer.

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

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

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

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Xi || = 2 N