Let U have a uniform distribution on the interval [0, 1]. Then observed values having this distribution

Question:

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 / λ)ln(1 - U).

a. Show that X has an exponential distribution with parameter λ. [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 λ = 10?

Distribution
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