Let X be a random variable distributed uniformly over [0, 20]. Define a new random variable Y

Question:

Let X be a random variable distributed uniformly over [0, 20]. Define a new random variable Y by Y = [X] (the greatest integer in X). Find the expected value of Y. Do the same for Z = [X + .5]. Compute E (|X − Y |) and E (|X − Z|). (Note that Y is the value of X rounded off to the nearest smallest integer, while Z is the value of X rounded off to the nearest integer. Which method of rounding off is better? Why?)