Let the random variable yn have a distribution that is b(n, p).
(a) prove that yn/n converges in probability to p. this result is one form of the weak law of large numbers.
(b) prove that 1 − yn/n converges in probability to 1 − p.
(c) prove that (yn/n)(1 − yn/n) converges in probability to p(1 − p).