Basic properties of PDFs and CDFs: (a) Why does Pr(a

Basic properties of PDFs and CDFs: (a) Why does Pr(a < X < b) = Pr(a X S b) if X is a continuous random variable? Give a counterexample to show that this is not true for a discrete random variable. (b) If f is a PDF, why does f (x)dx = 1? (c) Use the fundamental theorem of calculus in equation 5 to show that Pr(a < X S b) = F(b) - F(a) where F is the CDF of X.