Let X be a discrete random variable and Y an independent Uniform[0, 1] random variable. Show that the random variable Z = {X + Y } is also uniform and it is independent of X.Recall that {a} ∈ [0, 1) is the fractional part of a. {a} = a − ⌊a⌋ where ⌊a⌋ is the largest integer not bigger than a.