If y has a binomial distribution with n trials and success probability p, show that Y/n is a consistent estimator of p.
Can someone show how to show this. I appreciate it any and all help. thanks.
Basically both the procedures need same labour which is very little indeed. Since $\displaystyle Y\sim Bin(n,p)$, Obviously $\displaystyle E(Y)=np$ which gives $\displaystyle E(\frac{Y}{n})=p$ and $\displaystyle Var(Y)=np(1-p)$ , so $\displaystyle Var(\frac{Y}{n})=\frac{np(1-p)}{n^2} = \frac{p(1-p)}{n}\to\0$ as $\displaystyle n\to\infty$. No tough job