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)
The Attempt at a Solution
Note: when lim -> the limit of as n approaches infinity.
a) lim Yn/n = lim Yn * lim 1/n.
But the lim 1/n = 0 => lim Yn/n = 0. But it's supposed to converge to p.
Where did I make the mistake?