1.

(10 points total) A random variable, X, has a uniform probability density function defined as follows: f_X (x) = 1/3 for 1 x 2 and 0 otherwise. This random variable, X, is the input to the transformation y = g(x), defined as follows: y = 0 for x 0, 2x for 0 x 1, and 2 for x 1.

(a)(3 points) Obtain, sketch and accurately and completely label the probability distribution function, F_Y (y), of the output random variable Y .

(b)(3 points) Obtain, sketch and accurately and completely label the probability density function, f_Y (y), of the random variable Y .

(c) (4 points) What is E[Y ], the expected value of Y ?