Consider the Borel o-algebra B(R) on the real line R. Define the functionP, : B(R) - {0, 1} as (1, if0 EA follows (using indicator functions): P.(A):= 140) = 10. 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 6 be the Dirac delta function defined by the familiar equation f (x)6(x) dx =f(0) for any given f: R - R. Derive a formula for P. (A) (A E B(R)) in terms of 6. Note: This question shows how the Dirac delta function, which is not technically a function, can be formulated rigorously in the Kolmogorov framework in terms of a probability measure