Question: 123. Let U have a uniform distribution on the interval [0, 1]. Then observed values having this distribution can be obtained from a computers random

123. 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  (1/)ln(1  U).

a. Show that X has an exponential distribution with parameter . [Hint: The cdf of X is F(x)  P(X  x); X  x is equivalent to U  ?]

b. How would you use part

(a) and a random number generator to obtain observed values from an exponential distribution with parameter   10?

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