Suppose that the random variable, X, has the probability density function f(x) = e^x for x 0 and f(x) = 0 elsewhere.

If Y = [X] , where g(x) = [x] is the smallest integer greater than or equal to x.

example: g(1.2) = [1.2] = 2.

(a) As a random variable, what are the possible values of Y , i.e., the outcome space of Y .

(b)What is the probability mass function of Y ?

(c)What distribution does Y follow, and for which parameters?