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