Question: Let U U(0, 1). Let a and b be constants with a < b, and let X = (b a)U + a. a.

Let U ∼ U(0, 1). Let a and b be constants with a < b, and let X = (b − a)U + a.

a. Find the cumulative distribution function of U

b. Show that P(X ≤ x) = P(U ≤ (x −a)/(b−a)).

c. Use the result of part (b) to show that X ∼ U(a, b).

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