Question: Let U be U(0, 1)-distributed and let h: (0, 1) (0, ), h(u) = -log(u) We define X - h(U). := (a) (2 Points)

Let U be U(0, 1)-distributed and let h: (0, 1) (0, ),

Let U be U(0, 1)-distributed and let h: (0, 1) (0, ), h(u) = -log(u) We define X - h(U). := (a) (2 Points) Show that for any a E R we have {X a} = {U > e-}. (b) (2 Points) Find the distribution function F of X. Which known distribution does X have? (c) (2 Points) Find the expectation E(X) of X.

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