Question: Let X be a random variable with density function f (x) = ex, x > 0. Let Y be another variable defined by Y =

Let X be a random variable with density function f (x) = e−x, x > 0.

Let Y be another variable defined by Y =

{

X, if X ≤ 1, 1∕X, if X > 1.

Find the distribution function, the density function and the expectation of Y.

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