Let U have a uniform distribution on the interval [0, 1].

Then observed values having this distribution can be obtained from a computer’s random number generator. Let X 5 2(1/l)ln(1 2 U).

b r(x) 5 • aa1 2 x b

b 0 # x # b

a. Show that X has an exponential distribution with parameter . [Hint: The cdf of X is ;
is equivalent to ?]

b. How would you use part

(a) and a random number generator to obtain observed values from an exponential distribution with parameter ?