Let X be a continuous random variable whose distribution function F is strictly increasing throughout . Show that the random variable Y = [X], the

Let X be a continuous random variable whose distribution function F is strictly increasing throughout ℝ. Show that the random variable Y = [X], the integer part of X, is a discrete variable with probability function

fy(y) F(y+1) F(y), y Ry = {0, 1, 2,...}.