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## Homework Statement

Let the random variable Y

_{n}have the distribution b(n,p).

a)Prove that Y

_{n}/n converges in probability p.

b)Prove that 1 - Y

_{n}/n converges to 1 - p.

c)Prove that (Y

_{n}/n)(1 - Y

_{n}/n) converges in probability to p(1-p)

## Homework Equations

## The Attempt at a Solution

Note: when lim -> the limit of as n approaches infinity.

a) lim Y

_{n}/n = lim Y

_{n}* lim 1/n.

But the lim 1/n = 0 => lim Y

_{n}/n = 0. But it's supposed to converge to p.

Where did I make the mistake?