2. (12 pts.) Consider the Borel o-algebra B(R) on the real line R. Define the function P, : B(R) + {0,1} as follows (using indicator functions): Po(A) := La(0) = { 1 if O E A 0 otherwise. a. Show that (R, B(R), Po) is a probability space. b. Determine the CDF of Po, if it exists. Also determine the PDF of Po, if it exists. c. Let be the Dirac delta function defined by the familiar equation Ls(a)(x) dx = 10 for any given f : R + R. Derive a formula for Po(A) (A E B(R)) in terms of d