Let the random variable Yn have the distribution b(n,p).
a)Prove that Yn/n converges in probability p.
b)Prove that 1 - Yn/n converges to 1 - p.
c)Prove that (Yn/n)(1 - Yn/n) converges in probability to p(1-p)
So I need to use Chebyshev's inequality to solve it. E[Yn/n] = (1/n)*E[Yn] = (1/n)*(np) = p
Var[Yn/n] = (1/n^2)*Var(Yn) =(1/n^2)*(npq) = pq/n
and as n approaches infinity therefore Yn converges to p.
Is this correct?