Proving a distribution convergs to a standard normal distribution
Y has a binomial distribution based on n trials and success probability p. Then the point estimator (pn=Y/n) is an unbiased estimator of p. Prove that the distribution (pn-p)/sqr((pn*qn)/n) converges to a standard normal distribution.
I am supposed to the following theorem to prove it:
Suppose that Un has a distribution function that converges to a standard normal dist function as n-->∞. If Wn converges in probability to 1, then the dist. function Un/Wn converges to a Standard normal dist. function.
I am unsure of how to approach this so any help is greatly appreciated.